Surface Area: Pyramids and Cones - Glencoe

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To find the surface area of a pyramid, you must ... lateral surface of a pyramid is the area of the lateral faces (not including the base). ... Use the formula. SA r2.
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11-5 Surface Area: Pyramids and

Cones

(Pages 578–582)

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

Examples

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.

Find the surface area of the given geometric solids.

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

b. a cone with a radius of 4 cm and a slant height of 12 cm Use the formula. SA  r2  r SA  (4)2  (4)(12) SA  50.3  150.8 SA  201.1 cm2

Find the surface area of the base and the lateral faces. Base: Each triangular side: 1 2

1 2

A  s2 or (20)2

A   bh or  (20)(40)

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.

2.

3.

18.2 m 28.7 ft 10 ft

10 m

4.

12.3 mm

5.

11.4 in.

8 mm

10 ft

8 mm

6. 21 cm 3.1 in.

15.3 in.

2.2 in.

2.2 in.

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

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 ©

Glencoe/McGraw-Hill

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Glencoe Pre-Algebra