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11-5 Surface Area: Pyramids and

Cones

(Pages 578582)

A pyramid is a solid figure that has a polygon for a base and triangles for sides, or lateral faces. Pyramids have just one base. The lateral faces intersect at a point called the vertex. Pyramids are named for the shapes of their bases. For example, a triangular pyramid has a triangle for a base. A square pyramid has a square for a base. The slant height of a pyramid is the altitude of any of the lateral faces of the pyramid. To find the surface area of a pyramid, you must find the area of the base and the area of each lateral face. The area of the lateral surface of a pyramid is the area of the lateral faces (not including the base). A circular cone is another solid figure and is shaped like some ice cream cones. Circular cones have a circle for their base.

Surface Area of a Circular Cone The surface area of a cone is equal to the area of the base, plus the lateral area of the cone. The surface area of the base is equal to r 2. The lateral area is equal to r , where is the slant height of the cone. So, the surface area of the cone, SA, is equal to r 2 r .

Examples

Find the surface area of the given geometric solids. b. a cone with a radius of 4 cm and a slant height of 12 cm

Use the formula. SA SA SA SA r r2 (4)2 (4)(12) 50.3 150.8 201.1 cm2

a. a square pyramid with a base that is 20 m on each side and a slant height of 40 m

Find the surface area of the base and the lateral faces. Base: Each triangular side: A s2 or (20)2 A

1 1 bh or (20)(40) 2 2

A 400 SA 400 4(400) SA 2000 m2

A 400 Area of the base plus area of the four lateral sides.

Practice

Find the surface area of each solid. Round to the nearest tenth. 1.

18.2 m 28.7 ft 10 m 10 ft 10 ft 12.3 mm 8 mm 8 mm

2.

3.

4.

11.4 in.

5.

3.1 in. 15.3 in. 2.2 in. 2.2 in.

6.

21 cm 17 cm

7. Standardized Test Practice What is the surface area of a square pyramid where the length of each side of the base is 10 meters and the slant height is also 10 meters? A 300 m2 B 400 m2 C 500 m2 D 1000 m2

©

Glencoe/McGraw-Hill

Answers: 1. 885.9 m2 2. 674 ft2 3. 260.8 mm2 4. 548.0 in2 5. 18.5 in2 6. 2029.5 cm2 7. A

94

Glencoe Pre-Algebra

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