1. Quiz 1. the triangular pyramid 2. the cone Find the volume of each figure to the nearest tenth.Use 3.14 for . Find the surface area of each figure to the nearest tenth. Use 3.14 for . 3. the triangular prism 4. the cylinder

2. Pre-Algebra 6.9 Surface and Area of Pyramids and Cones

3. 1. A rectangular prism is 0.6 m by 0.4 m by 1.0 m. What is the surface area? 2. A cylindrical can has a diameter of 14 cm and a height of 20 cm. What is the surface area to the nearest tenth? Use 3.14 for . 2.48 m 2 1186.9 cm 2 Warm Up

4. Learn to find the surface area of pyramids and cones.

5. slant height regular pyramid right cone Vocabulary

6. The slant height of a pyramid or cone is measured along its lateral surface. In a right cone, a line perpendicular to the base through the tip of the cone passes through the center of the base. The base of a regular pyramid is a regular polygon, and the lateral faces are all congruent. Right cone Regular Pyramid

8. Find the surface area of each figure B. S = r 2 + rl = 20.16 ft 2 = (3 2 ) + (3)(6) = 27  84.8 cm 2 A. S = B + Pl 1212 = (2.4 2.4) + (9.6)(3) 1212 Example: Finding Surface Area

9. Find the surface area of each figure. = (3 3) + (12)(5) 1212 B. S = r 2 + rl = 39 m 2 = (7 2 ) + (7)(18) = 175  549.5 ft 2 5 m 3 m 7 ft 18 ft A. S = B + Pl 1212 Try This

10. A cone has diameter 8 in. and slant height 3 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius. They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height. Example: Exploring the Effects of Changing Dimensions

11. Original DimensionsTriple the Slant Height Triple the Radius S = r 2 + rl = (4.5) 2 + (4.5)(2) = 29.25in 2  91.8 in 2 S = r 2 + r(3l) = (4.5) 2 + (4.5)(6) = 47.25in 2  148.4 in 2 S = r) 2 + r)l = (13.5) 2 + (13.5)(2) = 209.25in 2  657.0 in 2 A cone has diameter 9 in. and a slant height 2 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius. They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height. Try This

12. The upper portion of an hourglass is approximately an inverted cone with the given dimensions. What is the lateral surface area of the upper portion of the hourglass? = (10)(27.9)  876.1 mm 2 Pythagorean Theorem Lateral surface area L = rl a 2 + b 2 = l 2 10 2 + 26 2 = l 2 l  27.9 Example: Application

13. A road construction cone is almost a full cone. With the given dimensions, what is the lateral surface area of the cone? = (4)(12.65)  158.9 in 2 12 in. 4 in. Pythagorean Theorem a 2 + b 2 = l 2 4 2 + 12 2 = l 2 l  12.65 Lateral surface area L = rl Try This

14. Find the surface area of each figure to the nearest tenth. Use 3.14 for . 1. the triangular pyramid 2. the cone 175.8 in 2 6.2 m 2 Lesson Quiz: Part 1

15. 3. Tell whether doubling the dimensions of a cone will double the surface area. It will more than double the surface area because you square the radius to find the area of the base. Lesson Quiz: Part 2