1. Holt Geometry 10-5 Surface Area of Pyramids and Cones 10-5 Surface Area of Pyramids and Cones Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Holt Geometry 10-5 Surface Area of Pyramids and Cones Warm Up Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = 24 2. c = 15, a = 9 3. b = 40, c = 41 4. a = 5, b = 5 5. a = 4, c = 8 c = 25 b = 12 a = 9

3. Holt Geometry 10-5 Surface Area of Pyramids and Cones Learn and apply the formula for the surface area of a pyramid. Learn and apply the formula for the surface area of a cone. Objectives

4. Holt Geometry 10-5 Surface Area of Pyramids and Cones vertex of a pyramid regular pyramid slant height of a regular pyramid altitude of a pyramid vertex of a cone axis of a cone right cone slant height of a right cone altitude of a cone Vocabulary

5. Holt Geometry 10-5 Surface Area of Pyramids and Cones The vertex of a pyramid is the point opposite the base of the pyramid. The base of a regular pyramid is a regular polygon, and the lateral faces are congruent isosceles triangles. The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.

6. Holt Geometry 10-5 Surface Area of Pyramids and Cones

7. Holt Geometry 10-5 Surface Area of Pyramids and Cones Example 1A: Finding Lateral Area and Surface Area of Pyramids Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. Round to the nearest tenth, if necessary.

8. Holt Geometry 10-5 Surface Area of Pyramids and Cones Example 1B: Finding Lateral Area and Surface Area of Pyramids Find the lateral area and surface area of the regular pyramid.

9. Holt Geometry 10-5 Surface Area of Pyramids and Cones The vertex of a cone is the point opposite the base. The axis of a cone is the segment with endpoints at the vertex and the center of the base. The axis of a right cone is perpendicular to the base.

10. Holt Geometry 10-5 Surface Area of Pyramids and Cones The slant height of a right cone is the distance from the vertex of a right cone to a point on the edge of the base. The altitude of a cone is a perpendicular segment from the vertex of the cone to the plane of the base.

11. Holt Geometry 10-5 Surface Area of Pyramids and Cones Example 2A: Finding Lateral Area and Surface Area of Right Cones Find the lateral area and surface area of a right cone with radius 9 cm and slant height 5 cm.

12. Holt Geometry 10-5 Surface Area of Pyramids and Cones Example 2B: Finding Lateral Area and Surface Area of Right Cones Find the lateral area and surface area of the cone.

13. Holt Geometry 10-5 Surface Area of Pyramids and Cones Check It Out! Example 2 Find the lateral area and surface area of the right cone.

14. Holt Geometry 10-5 Surface Area of Pyramids and Cones Exit Slip Find the lateral area and surface area of each figure. Round to the nearest tenth, if necessary. 1. a regular square pyramid with base edge length 9 ft and slant height 12 ft 2. a regular triangular pyramid with base edge length 12 cm and slant height 10 cm 3. a right cone with a diameter of 20 in and a height of 40 in L = 216 ft 2 ; S = 297 ft 2 L = 180 cm 2 ; S ≈ 242.4 cm 2