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

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

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%

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

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

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.

8-11 Surface Area of Pyramids and Cones

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 = 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.

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 = S = 105 in 2 S = B + Pl 1212 Use the formula. B= ½bh. Substitute. P = 3(7) = 21 Add. S = bh + Pl S = (7)(6) + (21)(8) ‏ The surface area is 105 square inches.

8-11 Surface Area of Pyramids and Cones Check It Out: Example 1A Find the surface area of the pyramid. S = S = 39 m 2 S = B + Pl 1212 S = (3 3) + (12)(5) ‏ 1212 Use the formula. B= lw. Substitute. P = 4(3) = 12 Add. 5 m 3 m S = lw + Pl 1212 The surface area is 39 square meters.

8-11 Surface Area of Pyramids and Cones Check It Out: Example 1B Find the surface area of the pyramid S = S = 42 in 2 S = B + Pl 1212 Use the formula. B= ½bh. Substitute. P = 3(4) = 12 Add. S = bh + Pl S = (4)(3) + (12)(6) ‏ in. 3 in. 4 in. 6 in. 4 in. The surface area is 42 square inches.

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.

8-11 Surface Area of Pyramids and Cones

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 ≈ S = r 2 + rl S ≈ (3.14)(3 2 ) + (3.14)(3)(10) ‏ S ≈ The surface area is about square centimeters. Substitute. Multiply. Add.

8-11 Surface Area of Pyramids and Cones Check It Out: Example 2 Find the surface area of the cone. Use 3.14 for . Use the formula. S ≈ S = r 2 + rl S ≈ (3.14)(4 2 ) + (3.14)(4)(10) ‏ S ≈ The surface area is about square centimeters. Substitute. Multiply. Add.

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

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  ft 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

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 ft 2 B. 816 ft 2 C. 480 ft 2 D. 240 ft 2 Lesson Quiz for Student Response Systems

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 ft 2 C ft 2 D ft 2 Lesson Quiz for Student Response Systems