Read Chapter 11 Resource Masters text version

Chapter 11 Resource Masters

Consumable Workbooks

Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide and Intervention Workbook Study Guide and Intervention Workbook (Spanish) Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) 0-07-827794-9 0-07-827795-7 0-07-827788-4 0-07-827790-6 0-07-827789-2 0-07-827791-4

Answers for Workbooks The answers for Chapter 11 of these workbooks

can be found in the back of this Chapter Resource Masters booklet.

Spanish Assessment Masters Spanish versions of forms 2A and 2C

of the Chapter 11 Test are available in the Pre-Algebra Spanish Assessment Masters (0-07-830412-1).

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with Glencoe Pre-Algebra. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240

ISBN: 0-07-827777-9 1 2 3 4 5 6 7 8 9 10 047 11 10 09 08 07 06 05 04 03 02 Pre-Algebra Chapter 11 Resource Masters

CONTENTS

Vocabulary Builder............................vii Lesson 11-1

Study Guide and Intervention ........................609 Skills Practice.................................................610 Practice ..........................................................611 Reading to Learn Mathematics ......................612 Enrichment .....................................................613

Lesson 11-6

Study Guide and Intervention ........................634 Skills Practice.................................................635 Practice ..........................................................636 Reading to Learn Mathematics ......................637 Enrichment .....................................................638

Lesson 11-2

Study Guide and Intervention ........................614 Skills Practice.................................................615 Practice ..........................................................616 Reading to Learn Mathematics ......................617 Enrichment .....................................................618

Lesson 11-7

Study Guide and Intervention ........................639 Skills Practice.................................................640 Practice ..........................................................641 Reading to Learn Mathematics ......................642 Enrichment .....................................................643

Lesson 11-3

Study Guide and Intervention ........................619 Skills Practice.................................................620 Practice ..........................................................621 Reading to Learn Mathematics ......................622 Enrichment .....................................................623

Chapter 11 Assessment

Chapter 11 Test, Form 1.........................645­646 Chapter 11 Test, Form 2A ......................647­648 Chapter 11 Test, Form 2B ......................649­650 Chapter 11 Test, Form 2C ......................651­652 Chapter 11 Test, Form 2D ......................653­654 Chapter 11 Test, Form 3.........................655­656 Chapter 11 Open-Ended Assessment............657 Chapter 11 Vocabulary Test/Review ..............658 Chapter 11 Quizzes 1 & 2..............................659 Chapter 11 Quizzes 3 & 4..............................660 Chapter 11 Mid-Chapter Test .........................661 Chapter 11 Cumulative Review......................662 Chapter 11 Standardized Test Practice...........................................663­664 Unit Test/Review (Ch 9­11)....................665­666

Lesson 11-4

Study Guide and Intervention ........................624 Skills Practice.................................................625 Practice ..........................................................626 Reading to Learn Mathematics ......................627 Enrichment .....................................................628

Lesson 11-5

Study Guide and Intervention ........................629 Skills Practice.................................................630 Practice ..........................................................631 Reading to Learn Mathematics ......................632 Enrichment .....................................................633

Standardized Test Practice Student Recording Sheet ..............................................A1 ANSWERS ................................................A2­A30

iii

Teacher's Guide to Using the Chapter 11 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 11 Resource Masters includes the core materials needed for Chapter 11. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Pre-Algebra TeacherWorks CD-ROM. Pages vii-viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. When to Use Give these pages to students before beginning Lesson 11-1. Encourage them to add these pages to their Pre-Algebra Study Notebook. Remind them to add definitions and examples as they complete each lesson.

Vocabulary Builder

When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson.

Reading to Learn Mathematics

One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques. When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students.

Study Guide and Intervention

Each lesson in Pre-Algebra addresses one or two objectives. There is one Study Guide and Intervention master for each lesson. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.

Enrichment

Skills Practice There is one master for each lesson. These provide computational practice at a basic level.

When to Use These masters can be used with students who have weaker mathematics backgrounds or need additional reinforcement.

There is one extension master for each lesson. These activities may extend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students' perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for use with all levels of students. When to Use These may be used as extra credit, short-term projects, or as activities for days when class periods are shortened.

Practice

There is one master for each lesson. These problems more closely follow the structure of the Practice and Apply section of the Student Edition exercises. These exercises are of average difficulty.

iv

Assessment Options

The assessment masters in the Chapter 11 Resource Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use.

Intermediate Assessment

· Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. · A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and free-response questions.

Chapter Assessment

Chapter Tests · Form 1 contains multiple-choice questions and is intended for use with basic level students. · Forms 2A and 2B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. · Forms 2C and 2D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with axes are provided for questions assessing graphing skills. · Form 3 is an advanced level test with free-response questions. Grids without axes are provided for questions assessing graphing skills. All of the above tests include a freeresponse Bonus question. · The Open-Ended Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment. · A Vocabulary Test, suitable for all students, includes a list of the vocabulary words in the chapter and ten questions assessing students' knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet.

Continuing Assessment

· The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of Pre-Algebra. It can also be used as a test. This master includes free-response questions. · The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which may appear on the standardized tests that they may encounter. This practice includes multiplechoice, grid-in, and open-ended questions. Bubble-in and grid-in answer sections are provided on the master.

Answers

· Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 600­601. This improves students' familiarity with the answer formats they may encounter in test taking. · The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. · Full-size answer keys are provided for the assessment masters in this booklet.

v

NAME ______________________________________________ DATE ____________ PERIOD _____

11

Reading to Learn Mathematics

Vocabulary Builder

Vocabulary Builder

This is an alphabetical list of key vocabulary terms you will learn in Chapter 11. As you study this chapter, complete each term's definition or description. Remember to add the page number where you found the term. Add these pages to your Pre-Algebra Study Notebook to review vocabulary at the end of the chapter. Vocabulary Term base Found on Page

Definition/Description/Example

cone

cylinder

SIH-luhn-duhr

edge

face

lateral area

LA-tuh-ruhl

lateral face

plane

polyhedron

PAH-lee-HEE-druhn

vii

NAME ______________________________________________ DATE ____________ PERIOD _____

11

Reading to Learn Mathematics

Vocabulary Builder

(continued)

Vocabulary Term precision

prih-SIH-zhuhn

Found on Page

Definition/Description/Example

prism

pyramid

significant digits

sihg-NIH-fih-kuhnt

similar solids

skew lines

SKYOO

slant height

solid

surface area

vertex

volume

viii

NAME ______________________________________________ DATE ______________ PERIOD _____

11-1 Study Guide and Intervention

Three-Dimensional Figures

Identifying Three-Dimensional Figures A prism is a polyhedron with two parallel bases. A pyramid is a polyhedron with one base. Prisms and pyramids are named by the shape of their bases, such as triangular or rectangular.

Example 1

E

Identify the solid. Name the bases, faces, edges, and vertices. triangular pyramid Any of the faces can be considered a base. faces: EFG, EGH, EFH, FGH

F G

H

edges: EF, EG, EH, FG, FH, GH vertices: E, F, G, H

Diagonals and Skew Lines Skew lines are lines that lie in different planes and do not intersect. A diagonal of a figure joins two vertices that have no faces in common.

Example 2

F E K J M

Identify a diagonal and name all segments that are skew to it.

G

diagonal: FM skew segments: EH, HG, JK, KL, EJ, GL

H L

Exercises

Identify each solid. Name the bases, faces, edges, and vertices. 1.

M N L R S J K

2.

H

For Exercises 3­4, use the rectangular prism in Example 2. 3. Identify a diagonal that could be drawn from point E. 4. Name all segments that are skew to the new diagonal.

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Glencoe Pre-Algebra

Lesson 11-1

NAME ______________________________________________ DATE ______________ PERIOD _____

11-1 Skills Practice

Three-Dimensional Figures

Identify each solid. Name the bases, faces, edges, and vertices. 1.

F L J K R S H G

2.

V U T

3.

F E

4.

P Q K D L N

S R

M

C

For Exercises 5­8, use the rectangular prism below.

M Q N L J P

H

K

5. Identify a diagonal. 6. Name four segments skew to LQ. 7. State whether NP and HM are parallel, skew, or intersecting. 8. Name a segment that does not intersect plane KLQP.

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-1 Practice

Three-Dimensional Figures

Identify each solid. Name the bases, faces, edges, and vertices. 1.

P M N K L E A H D C

2.

G

3.

U R

W T V S

For Exercises 4­7, use the rectangular prism below.

L H J K

4. Identify a diagonal. 5. Name four segments skew to JK.

G D E

F

6. State whether HJ and FG are parallel, skew, or intersecting.

7. Name a segment that does not intersect plane DGLH. 8. ARCHITECTURE A sketch shows the plans for a new observation tower at an amusement park. Each unit on the drawing represents 10 feet.

a. Draw a top view and find the area of the bottom section. b. At the center of the tower, there is a staircase landing every 15 feet. How many landings are in the tower?

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Glencoe Pre-Algebra

Lesson 11-1

B

F

NAME ______________________________________________ DATE

____________ PERIOD _____

11-1 Reading to Learn Mathematics

Three-Dimensional Figures

Pre-Activity

How are 2-dimensional figures related to 3-dimensional figures?

Do the activity at the top of page 556 in your textbook. Write your answers below. a. If you observed the Great Pyramid or the Inner Harbor and Trade Center from directly above, what geometric figure would you see? b. If you stood directly in front of each structure, what geometric figure would you see? c. Explain how you can see different polygons when looking at the same 3-dimensional figure.

Reading the Lesson

Write a definition and give an example of each new vocabulary word or phrase. Vocabulary 1. plane 2. solid 3. polyhedron 4. edge 5. vertex 6. face 7. prism 8. base 9. pyramid 10. skew lines Definition Example

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NAME ______________________________________________ DATE ______________ PERIOD _____

11-1 Enrichment

Perspective Drawings

To draw three-dimensional objects, artists make perspective drawings such as the ones shown below. To indicate depth in a perspective drawing, some parallel lines are drawn as converging lines. The dotted lines in the figures below each extend to a vanishing point, or spot where parallel lines appear to meet.

Vanishing Points

Railroad tracks

Cube

Cabinet

Draw lines to locate the vanishing point in each drawing of a box. 1. 2. 3.

4. The fronts of two cubes are shown below. Using point P as the vanishing point for both cubes, complete the perspective drawings of the cubes.

P

5. Find an example of a perspective drawing in a newspaper or magazine. Trace the drawing and locate a vanishing point.

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Glencoe Pre-Algebra

Lesson 11-1

NAME ______________________________________________ DATE ______________ PERIOD _____

11-2 Study Guide and Intervention

Volume: Prisms and Cylinders

Volume of Prisms To find the volume V of a prism, use the formula V = Bh, where B is the area of the base, and h is the height of the solid.

Example 1

a.

4 cm 6 cm 3 cm

Find the volume of each prism. b.

4m 5m 9.8 m

V V

Bh (3 6)4

V V

Bh

1 2

9.8 5 4

V 72 The volume is 72 cm3.

V 98 The volume is 98 m3.

r 2, times

Volume of Cylinders The volume V of a cylinder with radius r is the area of the base, the height h, or V r2h.

Example 2

V V V r2h

Find the volume of each cylinder.

2.2 ft

2.22 4.5 68.4

4.5 ft

The volume is about 68.4 ft3.

Exercises

Find the volume of each solid. If necessary, round to the nearest tenth. 1.

2.5 in. 2.5 in. 2.5 in. 6 mm 1.9 mm

2.

10 mm

3.

12 ft 12 ft 25 ft

4. rectangular prism: length 9 mm, width 8.2 mm, height 5 mm 5. triangular prism: base of triangle 5.8 ft, altitude of triangle 5.2 ft, height of prism 6 ft

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Glencoe/McGraw-Hill

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-2 Skills Practice

Volume: Prisms and Cylinders

Find the volume of each solid shown or described. If necessary, round to the nearest tenth. 1. 2.

28 m 10 in. 41 m 7 ft 4 ft 26 m

3.

5 in.

11 ft

4.

3 yd 8 yd 27 yd

5.

6.

12 ft 4 cm 12 ft 25 ft

15 cm

8 cm

7.

24 mm 15 mm

8.

5 in.

9.

10 cm

5 cm

4 in. 8 in.

10. rectangular prism: length 18 ft, width 9 ft, height 1 ft 11. triangular prism: base of triangle 22 yd, altitude of triangle 14 yd, height of prism 30 yd

12. Find the height of a cylinder with a radius of 12 inches and a volume of 3754.8 in3. Round to the nearest tenth.

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Glencoe/McGraw-Hill

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Glencoe Pre-Algebra

Lesson 11-2

NAME ______________________________________________ DATE ______________ PERIOD _____

11-2 Practice

Volume: Prisms and Cylinders

Find the volume of each solid shown or described. If necessary, round to the nearest tenth. 1.

5 cm

2.

5 in. 11 in. 8 cm 9 cm 2 in.

3.

19.2 ft 30 ft

4.

12 cm

5.

8m 16 m

6.

24 m

8 mm 3 mm

2.5 cm

14 cm

7.

9 mm

8.

9 in.

9.

2.5 cm

2 cm 1.4 cm

30 mm 19 mm 1.5 in.

10. rectangular prism: length 22.5 ft, width 12.5 ft, height 1.2 ft 11. triangular prism: base of triangle 17 cm, altitude of triangle 3 cm, height of prism 10.2 cm 12. Find the height of a rectangular prism with a length of 11 meters, a width of 0.5 meter, and a volume of 23.1 m3. 13. Find the height of a cylinder with a radius of 8.4 inches and a volume of 3546.7 in3. Round to the nearest tenth. 14. A cube is 8 inches on each side. What is the height of a cylinder having the same volume, if its radius is 4 inches? Round to the nearest tenth.

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Glencoe/McGraw-Hill

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE

____________ PERIOD _____

11-2 Reading to Learn Mathematics

Volume: Prisms and Cylinders

Pre-Activity

How is volume related to area?

Do the activity at the top of page 563 in your textbook. Write your answers below. a. Build three more rectangular prisms using 24 cubes. Enter the dimensions and base areas in a table. Prism

1 2 3 4

Length (units)

6

Width (units)

1

Height (units)

4

Area of Base (units2)

6

c. Make a conjecture about how the area of the base B and the height h are related to the volume V of a prism.

Reading the Lesson

Write a definition and give an example of each new vocabulary word or phrase. Vocabulary 1. volume 2. cylinder Definition Example

Helping You Remember

3. For each figure below, write out the longer version (showing how to determine the base area) of the formula for volume.

h w h b a h r

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Glencoe Pre-Algebra

Lesson 11-2

b. Volume equals the number of cubes that fill a prism. How is the volume of each prism related to the product of the length, width, and height?

NAME ______________________________________________ DATE ______________ PERIOD _____

11-2 Enrichment

Great Circles

The great circle on a sphere is the intersection of the sphere with a plane through the center. Both circles shown to the right are great circles. They are congruent and have circumferences that measure 2 r. Volume of sphere: V

4 3

r3 4 r2

Surface area of a sphere: S

Example

The The The The area of the great circle is about 211.24 m2. circumference of the great circle is about 51.52 m. surface area of the sphere is about 844.96 m2. volume of the sphere is about 2309.56 m3.

8.2 m

Solve. Round answers to the nearest hundredth. 1. Find the volume of a sphere with a radius of 4 meters. 2. Find the surface area of a sphere with a radius of 8 centimeters. 3. A hemispherical dome (half of a sphere) has a height of 32 meters. a. What is the volume of the dome? b. What is the surface area?

32 m

4. Find the volume of the grain silo shown below.

20 m

4m

5. A cold capsule is 12 millimeters long and 4 millimeters in diameter. Find the volume of medicine it can contain.

12 mm

4 mm

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-3 Study Guide and Intervention

Volume: Pyramids and Cones

Volume of Pyramids To find the volume V of a pyramid, use the formula V = Bh, where B is the area 3 of the base, and h is the height of the solid.

1

Example 1

a. V V V V

1 Bh 3

Find the volume of each pyramid.

6 ft

b. V V

1 Bh 3 1 3 1 3 1 2 1 2

3 in. 1 in. 8 in.

1 (7 7) h 3 1 (7 7)6 3

7 ft 7 ft

1 8 h 1 8 3

V V

98

4

The volume is 98 ft3.

The volume is 4 in3.

1

Volume of Cones To find the volume V of a cone, use the formula V = r 2h, where r is the radius 3 and h is the height of the solid.

Example 2

V V V

1 3 1 3

Find the volume of the cone. Round to the nearest tenth.

11 m

r2 h (4.3) 2 11

4.3 m

213.0 m3

The volume is about 213.0 m3.

Exercises

Find the volume of each solid. If necessary, round to the nearest tenth. 1.

3 in.

2.

1.6 m

3.

9.1 ft 1.9 ft

9 in. 9 in. 0.8 m

4. square pyramid: length 1.2 cm, height 5 cm 5. cone: diameter 4 yd, height 7 yd

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Glencoe/McGraw-Hill

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Glencoe Pre-Algebra

Lesson 11-3

NAME ______________________________________________ DATE ______________ PERIOD _____

11-3 Skills Practice

Volume: Pyramids and Cones

Find the volume of each solid. If necessary, round to the nearest tenth. 1.

7 ft 6 ft 4 in. 5 ft 7.5 m 7.5 m 4.5 in.

2.

16 m

3.

4.

7 yd 7 yd

5.

5 ft 12 ft 12 ft

6.

20 in.

2 yd

15 in. 18 in.

7.

20 ft

8.

22 mm

9.

14 cm

23 ft

6 mm

25 mm

15 cm

10. rectangular pyramid: length 7 ft, width 2.5 ft, height 8 ft 11. cone: radius 20 cm, height 30 cm 12. Find the height of a cone with a radius of 4 inches and a volume of 160.8 in3. Round to the nearest tenth

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-3 Practice

Volume: Pyramids and Cones

Find the volume of each solid. If necessary, round to the nearest tenth. 1.

17 in.

2.

3 yd

3.

18 ft

12 in. 12 in.

3 yd 16 ft

16 ft

4.

10 m

5.

4.1 cm

6.

10 m 12 m

7 cm 38 m 11 m

7. Find the volume of a rectangular pyramid with a length of 14 feet, a width of 12 feet, and a height of 9 feet. 8. Find the height of a rectangular pyramid with a length of 8.4 meters, a width of 7.8 meters, and a volume of 819 m3. 9. Find the height of a rectangular pyramid with a length of 9 meters, a width of 8 meters, and a volume of 518.4 m3. 10. CONTAINERS A cone with a diameter of 3 inches has a height of 4 inches. A 2-inch square pyramid is being designed to hold nearly the same amount of ice cream. What will be the height of the square pyramid? Round to the nearest tenth.

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Glencoe Pre-Algebra

Lesson 11-3

NAME ______________________________________________ DATE ______________ PERIOD _____

11-3 Reading to Learn Mathematics

Volume: Pyramids and Cones

Pre-Activity

How is the volume of a pyramid related to the volume of a prism?

Do the activity at the top of page 568 in your textbook. Write your answers below. a. Compare the base areas and compare the heights of the prism and the pyramid. b. How many times greater is the volume of the prism than the volume of one pyramid? c. What fraction of the prism volume does one pyramid fill?

Reading the Lesson

Write a definition and give an example of the new vocabulary word. Vocabulary 1. cone Definition Example

2. What is the relationship between the volume of a pyramid and the volume of a prism if both figures have the same base areas and heights? 3. What is the relationship between the volume of a cone and the volume of a cylinder if both figures have the same base areas and heights?

Helping You Remember

4. Write out in words an explanation for each step in finding the volume of the pyramid at the right. V V V V

©

27 yd 5 yd 8 yd

1 Bh 3 1 1 3 2 1 1 3 2

5 8 h 5 8 27

11 yd

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Glencoe/McGraw-Hill

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-3 Enrichment

Using Area and Volume

Solve. If neccessary, round to the nearest hundredth. 1. Mrs. Bartlett wants to put carpeting in a room that is 15 feet long and 12 feet wide. How many square feet of carpeting does she need? 2. Tom is making a cover for a box 4.5 feet long and 23 inches wide. What will be the area of the cover, in square feet?

3. How many 2-inch by 3-inch tickets can be cut from a 2-foot by 3-foot sheet of paper?

4. What is the area of the top of a tree stump that is 42 centimeters in diameter?

5. Mrs. Stabile has a one-story house that is 32 feet wide and 48 feet long. She plans to build an addition 12 feet by 16 feet. What will the total floor area of the house be then?

6. How many cubic meters of dirt must be removed when digging the foundation of a building if the excavation is 32 meters long, 12 meters wide, and 8 meters deep?

7. Mr. Mendez has a whirling sprinkler for watering his lawn. The sprinkler waters a circle with a radius of 12 meters. Find the area of the lawn that he can water at one time.

8. A cylindrical storage tank has a diameter of 6 meters and a height of 5 meters. What is the volume of the storage tank?

9. In Mr. Curin's living room there is a circular mirror with a diameter of 18 inches. What is the area of the mirror?

10. Find the cost of cementing a driveway 9 meters by 16 meters at $48 per square meter.

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Glencoe Pre-Algebra

Lesson 11-3

NAME ______________________________________________ DATE ______________ PERIOD _____

11-4 Study Guide and Intervention

Surface Area: Prisms and Cylinders

Surface Areas of Prisms To find the surface area S of a rectangular prism with length , width w, and height h, use the formula S 2 w 2 h 2wh. To find the surface area of a triangular prism, find the area of each face, then add to find the total surface area.

. S S S

Example 1

2 w 68.6 2 h 2(2.8)(2.1)

Find the surface area of the rectangular prism 2wh 2(2.8)(5.8) 2(2.1)(5.8)

2.8 ft 5.8 ft

The surface area is 68.6 ft2.

2.1 ft

Example 2

A w

Find the surface area of the triangular prism. bottom left side right side

9 14 6 14 10.3 14

1 2 2

126 84 144.2 54

6 cm 9 cm

10.3 cm

14 cm

A

1 bh 2

two bases 126

6 9

Total surface area

84

144.2

54

408.2

cm2

Surface Areas of Cylinders To find the surface area S of a cylinder with radius r and height h, use the formula S 2 r 2 2 rh.

Example 3

S 2 r2 S = 2 (4.6)2 S 306.4

Find the surface area of the cylinder. Round to the nearest tenth.

4.6 m

2 rh 2 (4.6)(6)

6m

The surface area is about 306.4 m2.

Exercises

Find the surface area of each solid. If necessary, round to the nearest tenth. 1.

14 in. 13 in.

2.

17 in. 8 in. 22 in. 15 in. 10 in.

3.

12 mm

8 mm

4. cube: side length 8.3 cm

5. cylinder: diameter 20 yd, height 22 yd

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Glencoe/McGraw-Hill

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-4 Skills Practice

Surface Area: Prisms and Cylinders

Find the surface area of each solid shown or described. If necessary, round to the nearest tenth. 1.

5 in. 9 in. 12 m 15 m

2.

8m

10 m 10 m

3.

14.9 ft

10 ft 20 ft 11 ft

4 in.

4.

4 in. 14 in. 16 in.

5.

4m 4m

6.

3.5 m 0.6 m

3.5 m 4m 4m

7.

8.

2.5 yd 6 mm 1.5 yd

9.

5 in.

9 mm

18 in.

1 yd

10. rectangular prism: length 17 yd, width 4.5 yd, height 3 yd 11. cylinder: radius 16 ft, height 42 ft 12. cylinder: diameter 20.2 cm, height 43 cm

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Glencoe Pre-Algebra

Lesson 11-4

NAME ______________________________________________ DATE ______________ PERIOD _____

11-4 Practice

Surface Area: Prisms and Cylinders

Find the surface area of each solid shown or described. If necessary, round to the nearest tenth. 1.

5 cm 25 in. 24 cm 60 cm 20 in. 9 in. 18.6 mm 26.9 in. 12 mm

2.

3.

11 mm

15 mm

4.

5.

4 ft 38 cm 36 ft

6.

18 mm 10 mm

20 cm

20 cm

7. rectangular prism: length 10.2 m, width 8.5 m, height 9.1 m 8. rectangular prism: length 15.4 cm, width 14.9 cm, height 0.8 cm 9. cylinder: radius 28 mm, height 32 mm 10. cylinder: diameter 1.6 ft, height 4.2 ft 11. DECORATING A door that is 30 inches wide, 84 inches high, and 1.5 inches thick is to be decoratively wrapped in gift paper. How many square inches of gift paper are needed? PACKAGING For Exercises 12 and 13, use the following information. A cardboard shipping container is in the form of a cylinder, with a radius of 6 centimeters and a volume of 8595.4 cubic centimeters. 12. Find the length of the shipping container. Round to the nearest tenth. 13. Find the surface area of the shipping container. Round to the nearest tenth.

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NAME ______________________________________________ DATE ______________ PERIOD _____

11-4 Reading to Learn Mathematics

Surface Area: Prisms and Cylinders

Pre-Activity

How is the surface area of a solid different than its volume?

Do the activity at the top of page 573 in your textbook. Write your answers below. a. For each box, find the area of each face and find the sum. b. Find the volume of each box. Are these values the same as the values you found in part a? Explain.

Reading the Lesson

Write a definition and give an example of the new vocabulary phrase. Vocabulary 1. surface area Definition Example

2. How is finding the surface area of a prism or cylinder different from finding the figure's volume?

Helping You Remember

3. How does drawing a net help you find the surface area of a prism or cylinder? Draw a prism or cylinder and its net to justify your answer.

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Lesson 11-4

NAME ______________________________________________ DATE ______________ PERIOD _____

11-4 Enrichment

Euler's Formula

Leonard Euler (oi'ler), 1707­1783, was a Swiss mathematician who is often called the father of topology. He studied perfect numbers and produced a proof to show that there is an infinite number of primes. He also developed the following formula, relating the numbers of vertices, faces, and edges of a polyhedron. Euler's formula: V V F E F E 2

V5 8 F5 6 E 5 12

number of vertices number of faces number of edges

Cube

For a cube, the following is true. V F E 2 8 6 14 12 14 2

Another name for a cube is hexahedron. Use Euler's formula to find the number of faces of each polyhedron. 1. V 4, E 6 2. V 6, E 12

Tetrahedron

Octahedron

3. V

12, E

30

4. V

20, E

30

Icosahedron

Dodecahedron

The suffix hedron comes from the Greek language meaning "face." Find the meaning of each of the following prefixes. 5. hexa 6. tetra 7. octa 8. icosa 9. dodeca

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-5 Study Guide and Intervention

Surface Area: Pyramids and Cones

Surface Area of Pyramids The sum of the areas of the lateral faces is the lateral area of a pyramid. The surface area of a pyramid is the sum of the lateral area and the base area.

slant height lateral face base

Example 1

Area of base A A s2 32 or 9

Find the surface area of the square pyramid. Area of each lateral face A A

1 bh 2 1 (3)(4.5) or 6.75 2

Lateral area 4(6.75) 27

4.5 cm

3 cm

3 cm

Total surface area

27

9 or 36 cm2.

slant height radius

Surface Area of Cones The surface area S of a cone with radius r and slant height can be found by using the formula S r r 2.

Example 2

S r r2

Find the surface area of the cone. Round to the nearest tenth. (7.7)2

11.2 in. 7.7 in.

S S

(7.7)(11.2) 457.2 in2

The surface area is about 457.2 in2.

Exercises

Find the surface area of each solid. If necessary, round to the nearest tenth. 1.

15 ft

2.

2.3 m 0.22 m

3.

9 cm

22 ft

22 ft

10 cm

10 cm

4.

7.8 mm 6 mm 6 mm 6 mm

5.

6.8 yd 8.6 yd

6.

10.8 mm 7.2 mm

A 15.6 mm2

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Glencoe Pre-Algebra

Lesson 11-5

NAME ______________________________________________ DATE ______________ PERIOD _____

11-5 Skills Practice

Surface Area: Pyramids and Cones

Find the surface area of each solid. If necessary, round to the nearest tenth. 1.

12 m

2.

12 ft

3.

42 in.

5m

5m

10 ft

10 ft 21 in.

21 in.

4.

2.9 ft

5.

8.6 in.

6.

30 cm 10 in. 7 cm

4.8 ft 4.8 ft

10 in. A 43 in2

7.

55 mm 45 mm

8.

18 in. 11 in.

9.

20 m 10 m

10. square pyramid: base side length 6.3 m, slant height 4 m 11. cone: diameter 16 yd, slant height 10 yd 12. cone: radius 14 cm, slant height 33 cm

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-5 Practice

Surface Area: Pyramids and Cones

Find the surface area of each solid. If necessary, round to the nearest tenth. 1.

15 cm

2.

1.5 m 2.5 m

3.

11 m 9m

9.2 cm 9.2 cm

1.5 m 1.5 m A = 1.0 m2 9m

9m A = 35.1 m2

4.

17.5 cm

5.

9.2 mm

6.

7.5 in. 4.5 in.

30 cm 4.2 mm

7.

10 ft

8.

9m 11 m 6 ft

9.

4.3 cm 5 cm 5 cm

6 ft

10. square pyramid: base side length 8.4 in., slant height 8.4 in. 11. cone: radius 9 ft, slant height 22 ft 12. cone: diameter 26 cm, slant height 15 cm 13. PAINTING A wooden structure at a miniature golf course is a square pyramid whose base is 5 feet on each side. The slant height is 4.75 feet. Find the lateral area to be painted. 14. BAKING A cone-shaped icicle on a gingerbread house will be dipped in frosting. The icicle is 1 centimeter in diameter and the slant height is 7 centimeters. What is its total surface area?

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Glencoe Pre-Algebra

Lesson 11-5

15. HISTORY The Great Pyramid in Egypt was built for the Pharaoh Khufu. The base of each side is 230 meters. The height from the base along the face to the top is 187 meters. Find the total surface area.

NAME ______________________________________________ DATE ______________ PERIOD _____

11-5 Reading to Learn Mathematics

Surface Area: Pyramids and Cones

Pre-Activity

How is surface area important in architecture?

Do the activity at the top of page 578 in your textbook. Write your answers below. a. The front triangle has a base of about 230 feet and height of about 120 feet. What is the area? b. How could you find the total amount of glass used in the pyramid?

Reading the Lesson

Write a definition and give an example of each new vocabulary phrase. Vocabulary 1. lateral face Definition Example

2. slant height

3. lateral area

4. How does the slant height of a pyramid differ from the height of the pyramid? Include a drawing to help explain your answer.

Helping You Remember

5. Prepare the script for a short presentation on how to find the surface areas of pyramids and cones. Be sure to include any necessary vocabulary terms in your explanation. You may wish to include diagrams with your presentation.

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NAME ______________________________________________ DATE ______________ PERIOD _____

11-5 Enrichment

Area of an Equilateral Triangle

The area of an equilateral triangle is the product of one fourth of the square of a side times the square root of 3 (which is approximately 1.732). A or A

1 2 s ( 4

s2 4

3)

(1.732) A

102 (1.732) 4 100 (1.732) 4

Example

43.3

10 cm

The area of the triangle is approximately 43.3 cm2.

Find the area of each equilateral triangle. Round each answer to the nearest tenth. 1.

5m

2.

3.

8 in.

15 mm

4.

3 yd

5.

5.1 cm

6.

4.3 m

7.

1 2 ­ ft 2

8.

PA-E-100F/7446

9.

9.3 cm

3 ­ yd 3

1

10.

0.8 m

11.

12.

0.74 m

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Glencoe Pre-Algebra

Lesson 11-5

5 ­ ft

2 3

NAME ______________________________________________ DATE ______________ PERIOD _____

11-6 Study Guide and Intervention

Similar Solids

Identify Similar Solids Solids are similar if they have the same shape and their corresponding linear measures are proportional.

Example 1

a.

Determine whether each pair of solids is similar.

50 6.25

50 ft 6.25 ft

28 3.5

Write a proportion comparing corresponding edge lengths. Find the cross products. Simplify.

50(3.5) 175

6.25(28) 175

28 ft

3.5 ft

The corresponding measures are proportional, so the pyramids are similar. b.

8 cm 10 cm 12 cm

8 12

10 14

Write a proportion comparing radii and heights. Find the cross products. Simplify.

14 cm

8(14) 112

12(10) 120

The radii and heights are not proportional, so the cylinders are not similar.

Use Similar Solids You can find missing measures if you know solids are similar.

Example 2

1 0.8 6 x

Find the missing measure for the pair of similar solids.

Write a proportion. Find the cross products. Simplify.

1 ft 0.8 ft 3 ft 6 ft 2.4 ft

1x x

0.8(6) 4.8

The missing length is 4.8 ft.

x

Exercises

Determine whether each pair of solids is similar. 1.

6 cm 6 cm 15 cm 10 cm 4 cm 4 cm

2.

11 in. 16 in. 22 in.

2.75 in. 4 in. 5.5 in.

Find the missing measure for each pair of similar solids. 3. x

2 ft

4.

16 in.

x

0.4 ft

0.5 ft

8.4 in.

10.5 in.

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-6 Skills Practice

Similar Solids

Determine whether each pair of solids is similar.

3 cm

15 cm

5 cm

4m 6m 3m

10 m 15 m 7.5 m

3.

4.

24 cm 9.6 cm 8 in. 12 in. 8 in. 3 in. 4 in. 3 in. 20 cm 8 cm

5.

5.4 m 3.6 m

6.

4 ft 1.5 ft

10 ft 2.4 m 2.4 m 1.6 m 1.6 m

4 ft

Find the missing measure for each pair of similar solids. 7.

21 in.

8.

x

15 in. 15 in. 21 in.

6.6 cm x 11 cm 16.5 cm

21 in.

9.

15 ft 12 ft x 8 ft

10.

3 yd 2.4 yd

x

2 yd

1.6 yd

1.8 yd

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Glencoe/McGraw-Hill

635

Glencoe Pre-Algebra

Lesson 11-6

1.

9 cm

2.

NAME ______________________________________________ DATE ______________ PERIOD _____

11-6 Practice

Similar Solids

Determine whether each pair of solids is similar. 1.

32 in. 160 in.

2.

6m 6m 4m 6m 15 m 4m 10 m 4m

48 in. 240 in.

3.

4.

10 m 5 ft 2 ft 2 ft 9 ft 20 ft 5m 28 m 14 m

9 ft

Find the missing measure for each pair of similar solids. 5.

32.4 ft 18 ft 8.4 mm 15 ft 15 ft

6.

x

2.7 mm 6.3 mm

x

7.

72 in. 45 in.

8.

x

39 cm 30 in. 27 cm 24 cm 35.1 cm 50.7 cm

x

PLAYGROUNDS For Exercises 9 and 10, use the following information. In the miniature village at the playground, the model of the old school building is 6.6 feet long, 3.3 feet wide, and 4.6 feet high. 9. If the real building was 80 feet long and 40 feet wide, how high was it? 10. What was the volume of the old school building in cubic feet?

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-6 Reading to Learn Mathematics

Similar Solids

Lesson 11-6 Pre-Activity

How can linear dimensions be used to identify similar solids?

Do the activity at the top of page 584 in your textbook. Write your answers below. a. The model boxcar is shaped like a rectangular prism. If it is 8.5 inches long and 1 inch wide, what are the length and width of the original train boxcar to the nearest hundredth of a foot? b. A model tank car is 7 inches long and is shaped like a cylinder. What is the length of the original tank car? c. Make a conjecture about the radius of the original tank car compared to the model.

Reading the Lesson

Write a definition and give an example of the new vocabulary word. Vocabulary 1. similar solids Definition Example

2. If two cylinders are similar, then their 3. If two cubes are similar, then their

and

are proportional. are proportional.

Helping You Remember

4. For each pair of solids listed in the table below, describe what measurements you would need to determine if the pair is similar. Pair of Solids

Rectangular Prisms Cylinders Square Pyramids Triangular Prisms Cones

Measurements Needed

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NAME ______________________________________________ DATE ______________ PERIOD _____

11-6 Enrichment

Reduced Triangle Principle

The following steps can be used to reduce the difficulty of a triangle problem by converting to easier side lengths. Step 1 Step 2 Step 3 Multiply or divide the three lengths of the triangle by the same number. Solve for the missing side of the easier problem. Convert back to the original problem.

Example 1

33 x

Example 2

x

7­ 2 55

1

33 and 55 are both multiples of 11.Reduce the problem to an easier problem by dividing the x side lengths by 11. Let y represent .

11

4

Multiply each side by 2. Let y represent 2x.

3

y y

5

15

32 9

y2 y2 y2 y y

52 25 16 4

82 64

152 225 289 17

y2 y2 y2 y

8

Now convert back.

x 11

Now convert back. 2x y x x

y 2 17 1 or 8 2 2

x x

11y 11(4) or 44

Use the reduced triangle method to find the value of x. 1.

75 x x 45 x 1

2.

30 72

3.

1­ 3

1

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-7 Study Guide and Intervention

Precision and Significant Digits

Precision and Significant Digits Use the following rules to determine the number of significant digits in a measurement. · If a number contains a decimal point, the number of significant digits is found by counting the digits from left to right, starting with the first nonzero digit and ending with the last digit. · If a number does not contain a decimal point, the number of significant digits is found by counting the digits from left to right, starting with the first digit and ending with last nonzero digit.

Example 1

Determine the number of significant digits in each measure. b. 41.06 grams 4 significant digits d. 0.09 liters 1 significant digit

a. 5.70 kilometers 3 significant digits c. 330 miles 2 significant digits

Compute Using Significant Digits · When adding or subtracting measurements, the sum or difference should have the same precision as the least precise measurement. · When multiplying or dividing measurements, the product or quotient should have the same number of significant digits as the measurement with the least number of significant digits.

Example 2

a. 8.94 ft 8.94 3.875 5.065

Calculate. Round to the correct number of significant digits. 3.875 ft

2 decimal places 3 decimal places

b. 10.04 m 10.04 2.1 21.084

2.1 m

4 significant digits 2 significant digits 5 significant digits

The least precise measurement, 8.94, has two decimal places. So, round 5.065 to two decimal places, 5.07 ft.

The answer cannot have more significant digits than the factors, so round 21.084 to 2 significant digits, 21 m2.

Exercises

Determine the number of significant digits in each measure. 1. 1360 m 2. 0.0042 mm 3. 980.7 in. 4. 700 g

Calculate. Round to the correct number of significant digits. 5. 3.004 mm 6.31 mm 7. 15 cL 0.45 cL 6. 227.0 ft 8. 45.11 km 300.5 ft 22.8 km

9. 1.0415 cm 0.228 cm 11. 0.875 kL 4.2 kL

10. 19.1 in. 2.05 in. 12. 1.6 mm 4 mm

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Glencoe Pre-Algebra

Lesson 11-7

NAME ______________________________________________ DATE ______________ PERIOD _____

11-7 Skills Practice

Precision and Significant Digits

Identify the precision unit of each measuring tool. 1.

0mm 10 20 30 40 50 60 70 80

2.

inches

1

2

3

Determine the number of significant digits in each measure. 3. 80.4 kg 4. 55 in. 5. 700 mi 6. 12.7 yd

7. 0.09 cm

8. 5.04 gal

9. 0.08000 km

10. 15.0 ft

11. 6 L

12. 1040 yd

13. 1200 mi

14. 11 mm

15. 1005 m

16. 1050 cm

17. 1500 in.

18. 1.5 mi

19. 0.0015 L

20. 0.01005 km

21. 9.025 ft

22. 8.86 s

Calculate. Round to the correct number of significant digits. 23. 40.25 in. + 12.5 in. 24. 51 mi ­ 0.9 mi

25. 7.6 cm + 1.04 cm + 2.35 cm

26. 180.4 ft 2.75 ft

27. 17.3 cm 8 cm

28. 0.2 gal + 1.0 gal + 0.75 gal

29. 1.2 cL + 11 cL + 3.4 cL

30. 5.030 km 4.001 km

31. 14.5 yd ­ 6.875 yd

32. 0.081 km 4 km

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Glencoe Pre-Algebra

NAME ______________________________________________ DATE ______________ PERIOD _____

11-7 Practice

Precision and Significant Digits

Determine the number of significant digits in each measure. 1. 400 mi 2. 1.15 cm 3. 80.015 km 4. 5 mm

5. 94.010 mm

6. 94.01 g

7. 94.1 yd

8. 0.0941 kg

13. 7.009 s

14. 0.8 m

15. 5 in.

16. 1.3 cm

Calculate. Round to the correct number of significant digits. 17. 15 gal + 2.5 gal 18. 225.4 mi 7.75 mi

19. 12.825 yd ­ 8.5 yd

20. 29.056 m + 11.0 m + 17.95 m

21. 6.00678 km 9 km

22. 40.02 cm 14.8 cm

23. 6 mL + 5.1 mL + 7.28 mL

24. 60.75 in. 22.80 in.

25. 21.6 km 19.9 km

26. 90.56 kL + 100.49 kL + 64.55 kL

27. 6000 m 2.7 m

28. 5.08 cm + 4.991 cm + 6.202 cm

29. MEASURING Gordon measured the width of the floor of a shed in two measurements. They were 30.0 inches and 28.25 inches. What is the total width of the shed? Round to the correct number of significant digits. 30. WINDOWS A new storefront window is 10.75 feet wide and 9.25 feet high. What is the area of the window? Round to the correct number of significant digits.

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Glencoe/McGraw-Hill

641

Glencoe Pre-Algebra

Lesson 11-7

9. 12.08 L

10. 3000.4 in.

11. 5009.0 min

12. 0.009 mi

NAME ______________________________________________ DATE ______________ PERIOD _____

11-7 Reading to Learn Mathematics

Precision and Significant Digits

Pre-Activity

Why are all measurements really approximations?

Do the activity at the top of page 590 in your textbook. Write your answers below. a. Measure several objects (book widths, paper clips, pens...) using each ruler. Use a table to keep track of your measurements. b. Analyze the measurements and determine which are most useful. Explain your reasoning.

Reading the Lesson

Write a definition and give an example of each new vocabulary word or phrase. Vocabulary 1. precision Definition Example

2. significant digits

3. When adding or subtracting measurements, the sum or difference should have the same precision as the least . 4. When multiplying or dividing measurements, the product or quotient should have the same number of significant digits as the measurement with the least .

Helping You Remember

5. Provide two examples of each of the numbers described in the table below.

a. Write a number with four significant digits, two of which are zero. b. Write a number with three significant digits, no decimal point, and three zeros. c. Write a number with two significant digits, a decimal point, and two zeros.

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NAME ______________________________________________ DATE ______________ PERIOD _____

11-7 Enrichment

Doug Williams

Washington Redskins African-American quarterback Doug Williams was chosen as the Most Valuable Player of Super Bowl XXII. Williams and his team established several post-season National Football League (NFL) records. With 35 points in the second period, they broke the record for the most points scored in a period. Williams tied the previous record of four touchdown passes in a period. Two of the passes were thrown to Ricky Sanders, one for 80 yards and one for 50 yards. Williams totaled 340 yards passing, breaking the record held by Joe Montana of San Francisco. Williams is a graduate of Grambling State University. Apply algebra to some plays in football. You will need to use the Pythagorean Theorem and your knowledge of the tangent ratio.

football field

[Insert art SPEC ENR-11-07C-827777]

100 yards

60°

Williams

20 yards

Sanders (initial position)

1. Suppose Doug Williams passed the ball to Ricky Sanders, who was initially 20 yards to the right of Williams. He threw the ball at the angle shown in the diagram above. How far did Sanders have to run in the direction shown to catch the pass? (Round to the nearest tenth.) 2. Using your answer and the information given in Exercise 1, determine how far Williams had to throw the ball in order to get it to Sanders. 3. If Williams cut the angle to 45°, would Sanders need to run a greater or shorter distance to catch the pass? Explain. 4. Walter Payton, an African-American running back for the Chicago Bears, was the alltime leading NFL rusher at the time he retired in 1987, with 16,726 yards. How many times would a player need to run from one goal line of a football field to the other goal line in order to run 16,726 yards? (Round to the nearest whole number.)

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643

Glencoe Pre-Algebra

Lesson 11-7

NAME

DATE

PERIOD SCORE

11

Chapter 11 Test, Form 1

Write the letter for the correct answer in the blank at the right of each question. For Questions 1­3, use the rectangular prism. 1. Identify a diagonal. A. FA B. FC C. AB D. GH 2. Choose the segment skew to AB. A. ID B. CD C. FA D. HI

G F B A D I H

1.

C

2.

3. Choose the segment that does not intersect plane ABCD. A. GB B. DI C. FA

D. FI

3.

4.

Find the volume of each solid. 5.

6 cm 8 cm 14 cm

A. 672 cm3 C. 168 cm3

B. 336 cm3 D. 224 cm3

5.

6. pyramid: base area 25 in2, height 9 in. A. 706.5 in3 B. 37.5 in3 C. 75 in3 7.

8 ft 21 ft

D. 150 in3 B. 1407.4 ft3 D. 351.9 ft3

6.

A. 2111.2 ft3 C. 527.8 ft3

7.

For Questions 8­11, find the surface area of each solid. 8.

5 in. 7 in.

A. 377.0 in2 C. 549.8 in2

B. 219.9 in2 D. 298.5 in2

8.

9.

2 cm 3 cm 5 cm

A. 43 cm2 C. 62 cm2

B. 86 cm2 D. 30 cm2

9.

10. square pyramid: base 64 cm2, slant height 12 cm A. 208 cm2 B. 256 cm2 C. 448 cm2

D. 192 cm2

10.

© Glencoe/McGraw-Hill

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Glencoe Pre-Algebra

Assessment

4. CONSTRUCTION Jack pours cylinder-shaped concrete support bases for bird baths with a radius of 7 inches and a height of 26 inches. What is the volume of one base? A. 1143.5 in3 B. 4002.4 in3 C. 1274.0 in3 D. 571.8 in3

NAME

DATE

PERIOD

11

Chapter 11 Test, Form 1

C. 125.7 cm2

(continued)

11. cone: radius 5 cm, slant height 6 cm A. 207.3 cm2 B. 94.2 cm2 12. Choose a prism from the table that is similar to the prism shown. A. prism A B. prism B C. prism C D. prism D 13. Find the missing measure for the pair of similar solids. A. 30 in. B. 37.5 in. C. 21 in. D. 45.7 in.

D. 172.8 cm2

Height 1 4 3 3 in. in. in. in.

11.

Prism Length Width

2 in. 2 in. 5 in.

A B C D

3 in. 10 in. 6 in. 9 in.

4 in.

1 4 3 3

in. in. in. in.

12.

10 in. x 15 in.

13.

14. HOBBIES A model of a car is 7 inches long, 3 inches high, and 4 inches wide. On the model, 1 inch represents 2 feet. How long is the actual car? A. 14 ft B. 7 ft C. 14 in. D. 8 ft Determine the number of significant digits in each measure. 15. 1903 kg A. 1 16. 1.30 m A. 1 B. 2 C. 3 D. 4

14.

15.

B. 2

C. 3

D. 4

16.

For Questions 17 and 18, calculate. Round to the correct number of significant digits. 17. 1.85 cm · 0.1 cm A. 0.2 cm2 18. 12.41 in. 9.1 in. A. 21.51 in. B. 0.185 cm2 C. 0.19 cm2 D. 0.1 cm2 17.

B. 21.5 in.

C. 22 in.

D. 21 in.

18.

19. Choose the measurement that is most precise. A. 13 mm B. 13 cm C. 1.3 m

D. 13 m

19.

20. LANDSCAPING A mural is 4.36 feet tall and 14 feet long. What is the area of the mural? Round to the correct number of significant digits. A. 61.04 ft2 B. 61.040 ft2 C. 61 ft2 D. 61.0 ft2 Bonus The capstone on the Washington Monument is shaped like a square pyramid. The square base is 3 feet long on each side, and the slant height is 5.4 feet. Find the lateral area of the capstone, to the nearest tenth.

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20.

B:

646

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Test, Form 2A

E D A

Write the letter for the correct answer in the blank at the right of each question. For Questions 1­3, use the figure at the right. 1. Identify the solid. A. triangular prism C. triangular pyramid 2. Segments AB and CG are A. skew. B. parallel.

B

B. rectangular prism D. rectangular pyramid

C

G

1.

C. intersecting.

D. planes.

2.

3. Choose a segment that does not intersect plane DEG. A. CG B. AD C. BC

D. BE

3.

4. STORAGE A storage area in Lisa's closet is shaped like a rectangular prism that is 38 1 inches high, 29 1 inches wide, and 17 inches deep. What

2 4

A. 9572 1 in3

16

B. 2857 3 in3

10

C. 7056 in3

D. 19,144 1 in3

8

4.

Find the volume of each solid. 5.

6 in.

A. 1058 in3 C. 3.2 in3

A = 23 in2

B. 138 in3 D. 46 in3

5.

6. cylinder: radius 9 in., height 48 in. A. 6107.3 in3 B. 4071.5 in3 7.

20 m

C. 12,214.5 in3

D. 2714.3 in3

6.

A. 3801.3 m3 C. 806.7 m3

11 m

B. 2534.2 m3 D. 230.4 m3

7.

For Questions 8­11, find the surface area of each solid. 8.

5 in. 5 in.

A. 500 in2 C. 207 in2

B. 785 in2 D. 314 in2

8.

9.

3 cm 4 cm 7 cm

A. 84 cm2 C. 61 cm2

B. 124 cm2 D. 122 cm2

9.

10. square pyramid: base edge 10 cm, slant height 14 cm A. 170 cm2 B. 380 cm2 C. 660 cm2

© Glencoe/McGraw-Hill

D. 470 cm2

10.

Glencoe Pre-Algebra

647

Assessment

is the volume of the storage area?

NAME

DATE

PERIOD

11

Chapter 11 Test, Form 2A

(continued)

11. cone: diameter 12 cm, slant height 12 cm A. 263.9 cm2 B. 226.2 cm2 C. 339.3 cm2 12. Choose a cone from the table that is not similar to the cone shown. A. cone A B. cone B C. cone C D. cone D 13. Find the missing measure for the pair of similar solids. A. 17 cm B. 8 cm C. 8 cm D. 9 cm

6m

D. 565.5 cm2

Cone A B C D Height Radius 3 12 4.5 9 m m m m 2 8 2.5 6 m m m m

11.

4m

12.

15 cm

x

12 cm 20 cm 20 cm 12 cm

13.

14. A model of a building is 50 cm long, 32 cm wide, and 175 cm high. On the model, 1 centimeter represents 15 meters. How tall is the actual building? A. 2625 m B. 750 m C. 480 m D. 2175 m For Questions 15­17, calculate. Round to the correct number of significant digits. 15. 6.40 ft 0.5 ft A. 3.2 ft2 16. 66.4 mi 17 mi A. 49 mi B. 3 ft2 C. 3.0 ft2 D. 3.3 ft2

14.

15.

B. 49.4 mi

C. 50 mi

D. 49.0 mi

16.

17. 32.407 cm 5.12 cm 4.6 cm A. 32.0 cm B. 32.9 cm

C. 32.93 cm

D. 33 cm

17.

18. LANDSCAPING A rectangular garden is 9.86 meters long and 8.5 meters wide. What is the area of the garden? Round to the correct number of significant digits. A. 83 m2 B. 83.8 m2 C. 84 m2 D. 83.81 m2 19. Omari built a frame for a patio that is 15 1 feet long and 10 feet wide.

2

18.

How much concrete does he need to fill the frame to a depth of 8 inches? A. 103 1 ft3

3

B. 105 2 ft3

3

C. 1240 ft3

D. 124 ft3

19.

20. IRRIGATION Water is stored in a cylindrical tank with a diameter of 34 feet and a height of 22 feet. What is the surface area of the tank? A. 2927.9 ft2 B. 2563.8 ft2 C. 4165.8 ft2 D. 4456.7 ft2 Bonus The Lincoln Memorial has 36 exterior columns. Each marble column is 44 feet tall and has a diameter of 7 feet 5 inches. What is the volume of marble in one column? If necessary, round to the nearest tenth.

© Glencoe/McGraw-Hill

20.

B:

648

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Test, Form 2B

B D A E

Write the letter for the correct answer in the blank at the right of each question. For Questions 1­3, use the figure at the right. 1. Identify the solid. A. rectangular pyramid C. rectangular prism 2. Segments DG and AC are A. skew. B. parallel.

B. triangular prism D. triangular pyramid

C

G

1.

C. intersecting.

D. planes.

2.

3. Choose a segment that does not intersect plane ABC. A. BE B. CG C. DG

D. DA

3.

4. FOOD The interior of Kendra's refrigerator is shaped like a rectangular prism that is 34 3 inches high, 26 inches wide, and 15 1 inches deep. What

4 2

A. 7052 1 in3

8

B. 14,004 1 in3

4

C. 13,260 3 in3

8

D. 18,806 3 in3

8

4.

Find the volume of each solid. 5.

9 in.

A. 38 in3 C. 131 in3

A = 29 in2

B. 87 in3 D. 261 in3

5.

6. cylinder: radius 7 in., height 42 in. A. 2155.1 in3 B. 1847.3 in3 7.

20 m

C. 6465.4 in3

D. 2058 in3

6.

A. 3015.9 m3 C. 9047.8 m3

12 m

B. 4523.9 m3 D. 251.3 m3

7.

For Questions 8­11, find the surface area of each solid. 8.

6 in. 6 in.

A. 452 in2 C. 1131 in2

B. 679 in2 D. 565 in2

8.

9.

4 cm 5 cm

A. 320 cm2 C. 166 cm2

7 cm

B. 80 cm2 D. 140 cm2

9.

10. square pyramid: base edge 6 cm, slant height 10 cm A. 96 cm2 B. 156 cm2 C. 120 cm2

© Glencoe/McGraw-Hill

D. 60 cm2

10.

Glencoe Pre-Algebra

649

Assessment

is the volume of the refrigerator?

NAME

DATE

PERIOD

11

Chapter 11 Test, Form 2B

(continued)

11. cone: diameter 6 cm, slant height 8 cm A. 210.4 cm2 B. 94.2 cm2 C. 103.7 cm2 12. Choose a cone from the table that is not similar to the cone shown. A. cone A B. cone B C. cone C D. cone D 13. Find the missing measure for the pair of similar solids. A. 8 cm B. 6 cm C. 12 cm D. 18 cm

6m

D. 75.4 cm2

Cone A B C D Height Radius 1.5 7.5 12 15 m m m m 1 5 9 10 m m m m

11.

4m

12.

12 cm x 12 cm 12 cm

18 cm

18 cm

13.

14. ARCHITECTURE A model of a building is 40 cm long, 32 cm wide, and 225 cm high. On the model, 1 centimeter represents 15 meters. How tall is the actual building? A. 2250 m B. 600 m C. 3375 m D. 4455 m For Questions 15­17, calculate. Round to the correct number of significant digits. 15. 7.50 ft 0.5 ft A. 4.0 ft2 16. 71.3 mi 18 mi A. 53.0 mi B. 3.75 ft2 C. 3.8 ft2 D. 4 ft2

14.

15.

B. 53 mi

C. 53.3 mi

D. 54 mi

16.

17. 31.303 cm 6.14 cm 3.5 cm A. 33.94 cm B. 33.943 cm

C. 33.9 cm

D. 34.0 cm

17.

18. STORAGE A shelf is 5.24 feet long and 1.5 feet wide. What is the area of the shelf? Round to the correct number of significant digits. A. 7.9 ft2 B. 7.860 ft2 C. 7.86 ft2 D. 7.8 ft2 19. CONSTRUCTION Hector is installing a pool in the shape of a rectangular prism. The pool is 15.2 meters long, 7.6 meters wide, and 1.8 meters deep. What is the volume of the pool? A. 115.5 m3 B. 313.1 m3 C. 207.9 m3 D. 216.6 m3 20. MANUFACTURING Water is stored in a cylindrical tank with a diameter of 36 feet and a height of 24 feet. What is the surface area of the tank? A. 2899.8 ft2 B. 4750.1 ft2 C. 3362.3 ft2 D. 2827.4 ft2 Bonus The Transamerica pyramid in downtown San Francisco has a square base that is 145 feet on each side. What is the lateral area of the building if the slant height is 856 feet? If necessary, round to the nearest tenth.

© Glencoe/McGraw-Hill

18.

19.

20.

B:

650

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Test, Form 2C

G F I H

For Questions 1 and 2, use the rectangular prism. 1. State whether FI and CD are parallel, skew, or intersecting.

1.

B C D

2. Name three planes that intersect vertex A.

A

2.

Find the volume of each solid. If necessary, round to the nearest tenth. 3.

4 cm

9 cm

4.

4 cm

3. 4.

6 cm

11 cm

5.

4 in. 8 in.

6. triangular pyramid: base area 42 in2, height 12 in.

5. 6.

For Questions 7­10, find the surface area of each solid. If necessary, round to the nearest tenth. 7.

4 cm 4.2 in. 5 cm 14 cm

8.

2.5 in.

7. 8.

9.

1.2 ft

10.

64 mm

9. 10.

1.6 ft 1.6 ft

27 mm

11. A skating area is made of a 4-inch thick rectangular slab of ice. Find the volume of the ice if the area is 35 feet wide and 54 feet long.

© Glencoe/McGraw-Hill

11.

651

Glencoe Pre-Algebra

Assessment

NAME

DATE

PERIOD

11

Chapter 11 Test, Form 2C

6 mm 54 mm 12 mm

(continued)

12. Determine whether the pair of solids is similar.

12.

96 mm

13. Find the missing measure for the pair of similar solids.

15 cm x

13.

9 cm

9 cm 15 cm 15 cm

For Questions 14­16, calculate. Round to the correct number of significant digits. 14. 25 in. 14.2 in. 14. 15. 20.11 m 16. 17.

15. 0.5 ft 7.8 ft 16. 31.409 m 6.14 m

17. Order 0.50 cm, 0.5 cm, 50 cm, and 0.005 cm from most to least precise. 18. REMODELING Mr. Jimenez is cutting a hole in a kitchen counter top so that he can install a sink. The rectangular sink is 36 inches long and 18 inches wide. He needs to make the hole smaller than the sink by 0.25 inch on all sides. How much less is the area of the hole than the area of the sink? Round to the correct number of significant digits. Determine whether each statement is sometimes, always, or never true. Explain. 19. A pyramid has three faces.

18.

19.

20. If the dimensions of a cylinder are doubled, the volume is 8 times greater. Bonus The surface area S of a sphere with radius r is given by the formula S 4 r2. The radius of Mars is about 2106 miles. What is the surface area of Mars? Round to the nearest tenth. Assume Mars is a perfect sphere.

© Glencoe/McGraw-Hill

20.

B:

652

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Test, Form 2D

For Questions 1 and 2, use the rectangular prism. 1. State whether FC and HC are parallel, skew, or intersecting. 2. Name three planes that intersect vertex F.

B A D G F I H

1.

2.

C

Find the volume of each solid. If necessary, round to the nearest tenth. 3.

4 cm 12 cm 6 cm 12 cm

4.

4 cm

3. 4.

5.

4 in. 7 in.

6. triangular pyramid: base area 45 in2, height 18 in.

5. 6.

For Questions 7­10, find the surface area of each solid. If necessary, round to the nearest tenth. 7.

4 cm 4.2 in. 5 cm 12 cm

8.

3 in.

7. 8.

9.

10.

64 mm

9. 10.

1.5 ft 25 mm 1.6 ft 1.6 ft

11. CONSTRUCTION Peter is buying sand to use as a 2 inch deep 11. base under a new rectangular brick patio for his restaurant. Find the volume of sand he needs if the patio will be 30 feet wide and 48 feet long.

© Glencoe/McGraw-Hill

653

Glencoe Pre-Algebra

Assessment

NAME

DATE

PERIOD

11

Chapter 11 Test, Form 2D

6m 54 m 12 m

(continued)

12. Determine whether the pair of solids is similar.

12.

108 mm

13. Find the missing measure for the pair of similar solids.

10 cm

13.

15 cm x

10 cm 18 cm 18 cm

For Questions 14­16, calculate. Round to the correct number of significant digits. 14. 21 in. 13.4 in. 14. 15. 16.409 m 16. 17.

15. 0.5 ft 5.6 ft 16. 12.00 m 3.25 m

17. Order 0.70 cm, 0.007 cm, 700 cm, and 0.7 cm from most to least precise.

18. REMODELING Mr. Rockwell is cutting a hole in a kitchen 18. counter top so that he can install a rectangular cooktop. The cooktop is 48 inches long and 22 inches wide. He needs to make the hole smaller than the cooktop by 0.25 inch on all sides. How much less is the area of the hole than the area of the cooktop? Round to the correct number of significant digits. Determine whether each statement is sometimes, always, or never true. Explain. 19. A polyhedron has two bases. 19.

20. If the dimensions of a cone are decreased by 1 , the volume is 1 the original volume. 8

2

20.

Bonus The surface area of a sphere is given by the formula S 4 r2. The radius of Earth is about 3963 miles at the equator. What is the surface area of Earth, to the nearest tenth? Assume Earth is a perfect sphere.

© Glencoe/McGraw-Hill

B:

654

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Test, Form 3

For Questions 1 and 2, use the figure shown at the right. 1. Draw the top view. 1.

2. If each unit on the drawing represents 6 inches, what is the height of the figure in feet? Find the volume of each solid. If necessary, round to the nearest tenth. 3. hexagonal prism: base area 15 ft2, height 10 in. 4.

6m 7m 15 cm 13 m 8m 8 cm

2.

3. 4.

5.

12 cm

6. triangular pyramid: base area 21 in2, height 6 in. For Questions 7­10, find the surface area of each solid. If necessary, round to the nearest tenth. 7. 8.

14 in. 5 2 in. 2.5 cm 6 cm 11.5 cm

1

6.

7. 8.

9.

10 ft

10.

2.4 ft

9. 10.

30 ft 3.2 ft 12 ft 3.2 ft

11. PAINTING Jonna wants to estimate the amount of paint needed to paint a mailbox. The mailbox is a rectangular prism with a dome-shaped top that is half of a cylinder. To the nearest tenth, what is the surface area of the mailbox to be painted? The underside of the mailbox does not need painting.

© Glencoe/McGraw-Hill

11.

1.2 ft U.S. Mail 3 ft 601 1.5 ft 2.4 ft

655

Glencoe Pre-Algebra

Assessment

5.

NAME

DATE

PERIOD

11

Chapter 11 Test, Form 3

(continued)

12. ARCHITECTURE The entrance hall to the Louvre Museum 12. in Paris is a glass and metal pyramid with a surface area of approximately 1980 square meters. The base of the pyramid is a square that is 35.4 meters on each side. What is the slant height of the pyramid? Round to the nearest hundredth. The base area is not included in the surface area.

For Questions 13­15, determine whether each pair of solids is sometimes, always, or never similar. Explain. 13. two cylinders 14. two spheres 15. a pyramid and a cone 16. Find the missing measures for the pair of solids.

8m 16 m

13. 14. 15. 16.

x y

3m

9m

For Questions 17­19, calculate. Round to the correct number of significant digits. 17. 3.769 cm 1.04 cm 18. 33.49 km 19. 30.7 g 4.9 km 17. 18. 19. 20.

0.3300 g

20. METALS A jeweler has three solid gold cylinders with radii 2.0 mm, 3.0 mm, and 4.0 mm. Each cylinder has a height of 10.0 mm. If he melts them down to make one cylinder, what will the volume of the new cylinder be? Round to the correct number of significant digits. Bonus A flood light projects a conical light beam to illuminate a sign. The volume of the light beam is 410 cubic feet. What is the diameter of the circle illuminated by the beam if the flood light is 15 feet from the billboard? Round to the nearest tenth.

© Glencoe/McGraw-Hill

B:

656

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Open-Ended Assessment

Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem. 1. Mr. Montoya's job is to estimate the labor and materials needed to paint commercial buildings. Part of his job is to determine the area to be painted. a. Explain how to find the area to be painted on the house at the right. 28 ft Do not include the roof. 20 ft

42 ft 24 ft

b. Explain how to find the surface area of the silo, including the roof. Find the area to the nearest tenth.

10 ft

30 ft

6 ft

c. Sometimes Mr. Montoya estimates the area to be painted because the actual area is difficult to determine. Would it be better for his estimates to be slightly greater than or slightly less than the actual area? Why? Estimate the surface area of the building at the right. Do not include the roof. 2. The Food and Drug Administration, among other duties, is charged with protecting consumers from misleading packaging. Many schemes have been used through the years to make customers believe they are getting more than they really are. a. Find the volume of the cylinder at the right. Find the volume if the height of the cylinder is doubled. Find the volume if the radius is doubled. Round your answers to the correct number of significant digits. Do you think retailers would tend to use tall bottles or large-diameter bottles to mislead customers? Why or why not? b. A way of misleading customers is by creating false bottoms such as those shown at the right. Guess which false bottom displaces the most volume. Find the volume of each false bottom to check your answer. Round your answers to the correct number of significant digits. 0.50 in. c. Give examples of other ways in which the actual volume of a container may be less than it appears to be.

20 ft 30 ft 50 ft 30 ft

2.0 ft

6.0 ft

1.0 in. 4.0 in. 4.0 in.

© Glencoe/McGraw-Hill

657

Glencoe Pre-Algebra

Assessment

NAME

DATE

PERIOD SCORE

11

Chapter 11 Vocabulary Test/Review

lateral area lateral face plane polyhedron precision prism pyramid significant digits similar solids skew lines slant height solid

base cone cylinder edge face greatest possible error

surface area vertex volume

Underline the term that best completes each statement. 1. A (prism, pyramid) is a solid with two bases. 2. A cone has one-third the volume of a (cylinder, prism) with the same base area and height. 3. Prisms and pyramids are named by the shape of their (bases, faces). 4. The measure of the space occupied by a solid region is the (surface area, volume). 5. A solid whose bases are congruent, parallel circles connected with a curved side is called a (cone, cylinder). 6. Surface area is measured in (cubic units, square units). 7. The altitude or height of each lateral face of a pyramid is called the (height, slant height). 8. Similar solids have the same (shape, size). 9. Significant digits indicate the (greatest possible error, precision) of the measurement. 10. If a prism has edges that are 3 times as long as the edges of another prism, then 3 is called the (scale factor, significant digit). In your own words-- Define each term. 11. skew lines

12. polyhedron

© Glencoe/McGraw-Hill

658

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Quiz

(Lessons 11­1 and 11­2)

Identify each solid. Name the faces, edges, and vertices. 1.

D C A

2.

G B E F H

J I

1.

2.

Find the volume of each prism or cylinder. If necessary, round to the nearest tenth. 3.

3 cm 7.3 cm 4 cm

4.

5m 3m

3. 4.

5. STANDARDIZED TEST PRACTICE Find the volume of the solid shown. A. 560 ft3 B. 680 ft3 C. 665 ft3 D. 5880 ft3

7 ft 10 ft

3 ft

5.

8 ft

NAME

DATE

PERIOD SCORE

11

Chapter 11 Quiz

(Lessons 11­3 and 11­4)

Find the volume of each solid. If necessary, round to the nearest tenth. 1. cone: radius 6 m, height 14 m 2. square pyramid: length 3.1 cm, height 2.4 cm Find the surface area of each solid. If necessary, round to the nearest tenth. 3.

3 in.

1. 2.

4.

12 m

3. 4.

3.8 in.

9m 10 m 7m

5. rectangular prism: length 10 cm, width 3 cm, height 2 cm

© Glencoe/McGraw-Hill

5.

Glencoe Pre-Algebra

659

Assessment

NAME

DATE

PERIOD SCORE

11

Chapter 11 Quiz

(Lessons 11­5 and 11­6)

Find the surface area of each solid. If necessary, round to the nearest tenth. 1.

1.8 ft

2.

6 8 in.

1

1. 2.

4 in. 1.6 ft 1.6 ft

Determine whether each pair of solids is similar. 3.

9 cm 6 cm

4.

5 in. 12 in.

2 cm 3 cm

3. 4.

3 in. 2 in. 6 in. 4 in.

Find the missing measure for the pair of similar solids. 5.

x 7.2 cm 3 cm 10.8 cm

5.

NAME

DATE

PERIOD SCORE

11

Chapter 11 Quiz

(Lesson 11­7)

Determine the number of significant digits in each measure. 1. 34.5 in. 2. 0.0040 mm For Questions 3 and 4, calculate. Round to the correct number of significant digits. 3. 6.2 mm 4. 4.10 mi 3.41 mm 0.25 mi 3. 4. 5. 1. 2.

5. MEASUREMENT Order 0.6 cm, 6 cm, 60 cm, 0.006 cm, and 0.60 cm from most to least precise.

© Glencoe/McGraw-Hill

660

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

11

Chapter 11 Mid-Chapter Test

(Lessons 11­1 through 11­4)

Part I Write the letter for the correct answer in the blank at the right of each question.

Find the volume of each solid. If necessary, round to the nearest tenth. 1. rectangular pyramid: length 13 ft, width 9 ft, height 20 ft A. 1770 ft3 B. 780 ft3 C. 1170 ft3 2. cone: radius 4 mm, height 7.5 mm A. 40 mm3 B. 377.0 mm3 D. 86.7 ft3 1.

C. 16.8 mm3

D. 125.7 mm3

2.

Find the surface area of each solid. If necessary, round to the nearest tenth. 3. cube: side length 8.5 m A. 433.5 m2 B. 289 m2 4.

4.8 in.

C. 614.1 m2

D. 578 m2

3.

{

7 in.

A. 123.7 in2 C. 141.7 in2

B. 36.2 in2 D. 117.1 in2

4.

5. rectangular prism: length 15 cm, width 7 cm, height 4 cm A. 193 cm2 B. 386 cm2 C. 420 cm2

D. 580 cm2

5.

Part II

Use the solid shown. 6. Identify the solid. Name the faces, edges, and vertices. 7. Identify all lines skew to DC.

D

A

6.

E B

7.

C

8. State whether AC and AB are parallel, skew, or intersecting.

8.

Find the volume of each solid. If necessary, round to the nearest tenth. 9.

7m

10.

11 cm

9. 10.

18 m 9 cm

7 cm

© Glencoe/McGraw-Hill

661

Glencoe Pre-Algebra

Assessment

NAME

DATE

PERIOD

11

Chapter 11 Cumulative Review

(Chapters 1­11)

6x 45.

(Lesson 3­5)

1. Solve 15

1.

2. Find the product of ( 11r2s7)(3rst4).

(Lesson 4­6)

2.

3. Solve 9x

7

47. (Lesson 7­6)

3.

4. Solve the system of equations y

(Lesson 8­9)

2x

1 and y

3x

1.

4.

5. Replace the with , , or 59 7.9 (Lesson 9­2)

to make a true statement.

5.

6. The lengths of the sides of a triangle are 14, 48, and 50. Is this triangle a right triangle? (Lesson 9­5)

6.

7. What is the area of a trapezoid with bases of 9 meters and 18 meters, and a height of 10 meters? (Lesson 10­5)

7.

8. Find the circumference of a circle with a radius of 8 meters.

(Lesson 10­7)

8.

9. What is the volume of a rectangular prism with a length of 8 meters, a width of 10 meters, and a height of 20 meters?

(Lesson 11­2)

9.

10. Nikki has a model of an Egyptian pyramid that has a slant height of 5 1 inches and a 3-inch square base. What is the 4 surface area of the pyramid?

(Lesson 11­5)

10.

11. Determine the number of significant digits in 10.40 m.

(Lesson 11­7)

11.

© Glencoe/McGraw-Hill

662

Glencoe Pre-Algebra

NAME

DATE

PERIOD

11

Standardized Test Practice

(Chapters 1­11)

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

1. Determine the domain of the relation {(4, 0), (7, 15), (0, 1)(9, 5)}.

(Lesson 1­6)

A. (0, 4, 7, 9)

B. (1, 4, 5, 15)

C. (0, 1, 5, 15)

D. (0, 4, 5, 9)

1.

A

B

C

D

2. Which verbal expression represents the phrase nine less than seven times a number? (Lesson 3­6) E. 7n 9 F. n 9 G. 9 7n H. 7 n 3. Write 0.36 as a fraction. A.

4 9

(Lesson 5­2)

9

2.

E

F

G

H

B. 9x 6

4 11

C.

36 100

D.

1 36

3.

A

B

C

D

5. Find the slope of the line that passes through the points A(­3, ­5) and B(1, ­1). (Lesson 8­4) A. 1 B.

3 2

C. ­1

D.

y

2 3

5.

A

B

C

D

6. Identify the linear inequality shown in the graph. (Lesson 8­10) E. y 3x ­ 5 F. y 3x ­ 5 G. y 3x ­ 5 H. y 3x ­ 5 7. Which set of numbers represents the lengths of the sides of a right triangle? (Lesson 9­5) A. 4, 4, 9 B. 5, 9, 12 C. 12, 16, 20

O

x

6.

E

F

G

H

D. 6, 7, 13

7.

A

B

C

D

8. Find the distance between the points Q(10, ­8) and R(­15, 7). Round to the nearest tenth. (Lesson 9­6) E. 15.8 F. 29.2 G. 14.1 H. 20.0 9. Frank draws two similar triangles. One triangle has sides of 8, 9, and 10 centimeters. The shortest side of the second triangle is 20 centimeters long. Find the length of the longest side of the second triangle. (Lesson 9­7) A. 26 cm B. 28 cm C. 25 cm D. 22 cm 10. Identify the transformation in the graph at the right. (Lesson 10­3) E. translation F. reflection G. rotation H. horizontal

y

8.

E

F

G

H

9.

A

B

C

D

O

x

10.

E

F

G

H

© Glencoe/McGraw-Hill

663

Glencoe Pre-Algebra

Assessment

4. Solve E. x

54. (Lesson 7­5) F. x 6

G. x

4

H. x

6

4.

E

F

G

H

NAME

DATE

PERIOD

11

Standardized Test Practice

(continued)

11. Find the area of a trapezoid with bases of 12 inches and 10 inches and a height of 15 inches. (Lesson 10­5) A. 74 in2 B. 165 in2 C. 330 in2 D. 66 in2 12. Find the radius of a circle if its circumference is 50.24 meters.

(Lesson 10­7)

11.

A

B

C

D

E. 4 m

F. 32 m

G. 16 m

H. 8 m

12.

E

F

G

H

13. Identify the solid. (Lesson 11­1) A. triangular prism B. square pyramid C. cone D. triangular pyramid 14. Find the volume of a rectangular prism with length of 12 inches, width of 9 inches, and height of 6 inches. (Lesson 11­2) E. 648 in3 F. 324 in3 G. 468 in3 H. 126 in3 15. Roger has a cone-shaped cotton candy container that is 12 inches high and has a radius of 6 inches. Find the volume of the container. (Lesson 11­3) A. 72 in3 B. 1357.2 in3 C. 452.4 in3 D. 432 in3 Part 2: Grid In

13.

A

B

C

D

14.

E

F

G

H

15.

A

B

C

D

Instructions: Enter your answer by writing each digit of the answer in a column box and then shading in the appropriate oval that corresponds to that entry.

16. Find the value of cos S to the nearest hundredth. (Lesson 9­8)

5m

S

11 m

16.

. / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

17.

. 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

17. Find the surface area in square inches of a soup can that has a

(Lesson 11­4)

T

4 6m

R

diameter of 3 inches and a height of 4

1 inches. 2

1 2 3 4 5 6 7 8 9

Part 3: Short Response

Instructions: Write your answer in the blank at the right of each question.

18. Find the percent of change in the price of a computer from $1145 to $1420. State whether the change is an increase or decrease. (Lesson 6­8) 19. Order 900, 0.90, 0.900, and 0.9 from most to least precise. Which number has the most significant digits? (Lesson 11­7)

© Glencoe/McGraw-Hill

18.

19.

664

Glencoe Pre-Algebra

NAME

DATE

PERIOD SCORE

Unit 4 Test

(Chapters 9­11)

1. Order 7.13, 29 ,

4 1 from least to greatest. 5

U V W

50, 7

1. 2.

2. Use a protractor to find the measure of UVW. Then classify the angle as acute, obtuse, right, or straight.

3. The measures of the angles of RST are in the ratio 2:3:5. Find the measure of each angle, and classify the triangle as acute, right, or obtuse. 4. Find the missing measure to the nearest tenth.

x

24 ft

3.

4.

18 ft

6. Find the distance between the points H(15, 3) and G( 10, 1). Round to the nearest tenth, if necessary. 7. On a small scale drawing, the length of the front of the public library is 12 centimeters, and the length of the front of the high school is 13 centimeters. On a larger scale drawing, the length of the library is 18 centimeters. Find the length of the high school on the larger drawing. 8. Tom rests a 32-foot ladder against a wall. The ladder forms a 61 angle with the ground. How high up the wall is the ladder? 9. Angles R and S are complementary. Find m R if m S 10. Find the measure of BA if ABC DEC.

B D

10 9 12

6.

7.

8.

78 .

9. 10.

C

6

15

A

E

11. The vertices of a figure are W( 2, 3), X(0, 5), Y(3, 1), and Z( 3, 4). What are the vertices of the transformed image after a reflection over the x-axis? 12. Find the value of x. Then find the missing angle measures.

x

70 70

11.

12.

x

© Glencoe/McGraw-Hill

665

Glencoe Pre-Algebra

Assessment

5. The lengths of the sides of a triangle are 9, 9, and 15. Determine whether this is a right triangle.

5.

NAME

DATE

PERIOD

Unit 4 Test

(Chapters 9­11)

(continued)

13. Find the area of a trapezoid with height 6 centimeters and bases 8 centimeters and 4 centimeters. 14. Find the sum of the measures of the interior angles of an octagon. 15. Find the circumference and area of a circle if its diameter is 12 feet. Round to the nearest tenth. 16. Find the area of the figure at the right to the nearest tenth, if necessary.

6 cm

13.

14.

15.

16.

15 cm

For Questions 17 and 18, find the volume of each solid. If necessary, round to the nearest tenth. 17. cylinder: radius 4.2 cm, height 9 cm 18. cube: side 8.5 in. 19. Julian owns an ice cream parlor. For pricing purposes, he needs to know how much ice cream a waffle cone holds. The cone is 5 1 inches deep and has a diameter of 3 inches. What

2

17. 18. 19.

is the volume of the waffle cone? If necessary, round to the nearest tenth. 20. Find the volume of the solid at the right. Round to the correct number of significant digits.

10 m

20.

15 m 8.1 m

For Questions 21­24, find the surface area of each solid. If necessary, round to the nearest tenth. 21. rectangular prism: height 9 ft, width 11 ft, length 21 ft 22. cylinder: height 20 in., diameter 16 in. 23.

9.5 m 4m

21. 22.

24.

3 cm

3 cm

23. 24.

3 cm

4 cm

25. A model of a building is 18 inches long, 15 inches wide and 24 inches high. On the model, 1 inch represents 12 feet. How tall is the actual building in feet?

© Glencoe/McGraw-Hill

25.

666

Glencoe Pre-Algebra

NAME

DATE

PERIOD

11

Standardized Test Practice

Student Record Sheet

(Use with pages 600­601 of the Student Edition.)

Part 1 Multiple Choice

Select the best answer from the choices given and fill in the corresponding oval. 1 2 3

A B C D

4 5 6

A

B

C

D

7 8

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

Part 2 Short Response/Grid In

Solve the problem and write your answer in the blank. For Questions 11, 12, 14, 15, 19, and 20, also enter your answer by writing each number or symbol in a box. Then fill in the corresponding oval for that number or symbol. 9 10 11 12 13 14 15 16 17 18 19 20

(grid in) (grid in) (grid in)

11

. 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

12

. 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

14

. 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

(grid in)

15

. 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

19

. 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

20

. 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 / . 0 1 2 3 4 5 6 7 8 9 . 0 1 2 3 4 5 6 7 8 9

(grid in)

(grid in)

Part 3 Open Ended

Record your answers for Question 21 on the back of this paper.

© Glencoe/McGraw-Hill

A1

Glencoe Pre-Algebra

Answers

Information

Chapter 11 Resource Masters

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