1. 8-11 Surface Area of Pyramids and Cones Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 8-11 Surface Area of Pyramids and Cones Warm Up Find the perimeter or circumference of each figure. Use 3.14 for . 1. 2. 30 cm 138.16 ft

3. 8-11 Surface Area of Pyramids and Cones Problem of the Day In a survey, 69 people were asked whether they prefer hamburgers or hot dogs. Thirty-three people said they prefer hot dogs. What percent of the people surveyed said they prefer hamburgers? about 52%

4. 8-11 Surface Area of Pyramids and Cones MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones. Also MA.7.G.2.2 Sunshine State Standards

5. 8-11 Surface Area of Pyramids and Cones Vocabulary regular pyramid slant height of a pyramid slant height of a cone

6. 8-11 Surface Area of Pyramids and Cones The diagram shows a square pyramid. The blue dashed line labeled l is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base. The base of a regular pyramid is a regular polygon, and the faces are congruent isosceles triangles.

7. 8-11 Surface Area of Pyramids and Cones

8. 8-11 Surface Area of Pyramids and Cones Additional Example 1A: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. S = 81 + 180 S = 261 m 2 S = B + Pl 1212 S = (9 9) + (36)(10) ‏ 1212 Use the formula. S = lw + Pl 1212 B = lw Substitute. P = 4(9) = 36 Add. The surface area is 261 square meters.

9. 8-11 Surface Area of Pyramids and Cones Additional Example 1B: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. S = 62.28 + 108 S = 170.28 S = B + Pl 1212 Use the formula. B= ½bh. S = bh + Pl 1212 1212 S = (12)(10.38) + (36)(6) ‏ 1212 1212 The surface area is 170.28 m 2.

10. 8-11 Surface Area of Pyramids and Cones Check It Out: Example 1A Find the surface area of each pyramid. = 217 mm 2 S = 49 + 168 = 217 S = B + Pℓ =(7)(7) + (28)(12) 1212 1212

11. 8-11 Surface Area of Pyramids and Cones Check It Out: Example 1B Find the surface area of the pyramid S = 94.8 = 94.8 m 2 S = B + Pℓ 1212 S =27.6 + (8+8+8)(5.6) = 27.6 + 67.2 1212 B = (8)(6.9) = 27.6 1212

12. 8-11 Surface Area of Pyramids and Cones The diagram shows a cone and its net. The blue dashed line is the slant height of the cone, the distance from the vertex to a point on the edge of the base.

13. 8-11 Surface Area of Pyramids and Cones

14. 8-11 Surface Area of Pyramids and Cones Additional Example 2: Finding the Surface Area of a Cone Find the surface area of the cone. Use 3.14 for . Use the formula. S ≈ 122.46 S = r 2 + rl S ≈ (3.14)(3 2 ) + (3.14)(3)(10) ‏ S ≈ 28.26 + 94.2 The surface area is about 122.46 square centimeters. Substitute. Multiply. Add.

15. 8-11 Surface Area of Pyramids and Cones Check It Out: Example 2A Find the surface area of the cone. Use 3.14 for . S ≈ 62.8 ft 2 S = r 2 + rℓ ≈ 3.14(2) 2 + 3.14 (2)(8) S ≈ 12.56 + 50.24 ‏

16. 8-11 Surface Area of Pyramids and Cones Check It Out: Example 2B The dimensions of the cone from Exercise 2a quadrupled. Find the surface area of the cone. Use 3.14 for . ≈ 1,004.8 ft 2 S = r 2 + rℓ S ≈ 200.96 + 803.84 ‏ S ≈ 3.14(8) 2 + 3.14 (8)(32)

17. 8-11 Surface Area of Pyramids and Cones Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

18. 8-11 Surface Area of Pyramids and Cones Lesson Quiz 1. Find the surface area of the pyramid. 2. Find the surface area of the cone. Use 3.14 for . 219.8 ft 2 236.25 m 2 3. A house being built is to have a roof in the shape of a square pyramid. The sides of the square base are 21 feet long and the slant height will be 12 feet. What will the surface area of the roof be? (Hint: The base of the pyramid is not part of the roof.) ‏ 504 ft²

19. 8-11 Surface Area of Pyramids and Cones 1. Find the surface area of a regular pyramid with a base of 12 feet by 12 feet and a slant height of 14 feet. A. 2016 ft 2 B. 816 ft 2 C. 480 ft 2 D. 240 ft 2 Lesson Quiz for Student Response Systems

20. 8-11 Surface Area of Pyramids and Cones 2. Find the surface area of a cone with a radius of 3 feet and a slant height of 6 feet. Use 3.14 for . A. 18 ft 2 B. 56.52 ft 2 C. 75.36 ft 2 D. 84.78 ft 2 Lesson Quiz for Student Response Systems