1. 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

2. Surface Areas and Volumes of Pyramids and Cones Sections 12-5, 12-6, 13-2

3. Pyramids 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.

4. Lateral and Surface Areas of Pyramids The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid. L = ½P l and SA = ½P l + B

5. Example: 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.

6. Cones 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. The axis of an oblique cone is not perpendicular to the base.

7. Lateral and Surface Areas of 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. L = ½P l and SA = ½P l + B

8. Example: Finding Lateral Area and Surface Area of Right Cones Find the lateral area and surface area of the cone.

9. Example: Find the lateral area and surface area of the right cone.

10. Volume of Pyramids and Cones

11. Example: Finding Volumes of Pyramids Find the volume of the square pyramid with base edge length 9 cm and height 14 cm.

12. Example: Finding Volumes of Cones Find the volume of a cone.

13. Example 3 Find the volume of the cone.

14. Lesson Quiz: Find the volume of each figure. Round to the nearest tenth, if necessary. 1. a rectangular prism with length 25 cm, width 17 cm, and height 21 cm 2. a cone with diameter 22 cm and height 30 cm 3. a cone with base circumference 8 m and a height of 7 m 4. a square pyramid with a base side length of 12 m and a height of 15 m V = 8925 cm 3 V = 3801.3 cm 3 V = 117.3 3 V = 720 m 3