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## Warm Up

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**Warm Up**Problem of the Day Lesson Presentation Lesson Quizzes**Warm Up**Find the perimeter or circumference of each figure. Use 3.14 for . 1. 2. 30 cm 138.16 ft**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%**Sunshine State Standards**MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones. Also MA.7.G.2.2**Vocabulary**regular pyramid slant height of a pyramid slant height of a cone**The base of a regular pyramid is a regular polygon, and the**faces are congruent isosceles triangles. 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.**1**2 S = lw + Pl 1 2 S = (9 • 9) + (36)(10) Additional Example 1A: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B = lw Substitute. P = 4(9) = 36 S = 81 + 180 Add. S = 261 m2 The surface area is 261 square meters.**1**2 1 2 S = bh + Pl 1 2 1 2 S = (7)(6) + (21)(8) Additional Example 1B: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B= ½bh. Substitute. P = 3(7) = 21 S = 21 + 84 Add. S = 105 in2 The surface area is 105 square inches.**5 m**1 2 S = lw + Pl 3 m 3 m 1 2 S = (3 • 3) + (12)(5) Check It Out: Example 1A Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. B= lw. Substitute. P = 4(3) = 12 S = 9 + 30 Add. S = 39 m2 The surface area is 39 square meters.**4 in.**1 2 1 2 S = bh + Pl 1 2 1 2 S = (4)(3) + (12)(6) 6 in. 4 in. 4 in. 3 in. Check It Out: Example 1B Find the surface area of the pyramid 1 2 S = B + Pl Use the formula. B= ½bh. Substitute. P = 3(4) = 12 S = 6 + 36 Add. S = 42 in2 The surface area is 42 square inches.**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.**Additional Example 2: Finding the Surface Area of a Cone**Find the surface area of the cone. Use 3.14 for . S = r2 + rl Use the formula. S ≈ (3.14)(32) + (3.14)(3)(10) Substitute. S ≈ 28.26 + 94.2 Multiply. S ≈ 122.46 Add. The surface area is about 122.46 square centimeters.**Check It Out: Example 2**Find the surface area of the cone. Use 3.14 for . S = r2 + rl Use the formula. S ≈ (3.14)(42) + (3.14)(4)(10) Substitute. S ≈ 50.24 + 125.6 Multiply. S ≈ 175.84 Add. The surface area is about 175.84 square centimeters.**Lesson Quizzes**Standard Lesson Quiz Lesson Quiz for Student Response Systems**Lesson Quiz**1. Find the surface area of the pyramid. 2. Find the surface area of the cone. Use 3.14 for . 236.25 m2 219.8 ft2 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**Lesson Quiz for Student Response Systems**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 ft2 B. 816ft2 C. 480ft2 D. 240 ft2**Lesson Quiz for Student Response Systems**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. 18ft2 B. 56.52 ft2 C. 75.36ft2 D. 84.78ft2