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8-7 Surface Area of Prisms and Cylinders Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Warm Up 1. A triangular pyramid has a base area of 1.2 m 2 and a height of 7.5 m. What is the volume of the pyramid? 2. A cone has a radius of 4 cm and a height of 10 cm. What is the volume of the cone to the nearest cubic centimeter? Use 3.14 for . 3 m 3 167 cm 3 Course 3 8-7 Surface Area of Prisms and Cylinders

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Problem of the Day An ice cream cone is filled halfway to the top. The radius of the filled part is half the radius at the top. What fraction of the cone’s volume is filled? Course 3 8-7 Surface Area of Prisms and Cylinders 1818

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Learn to find the surface area of prisms and cylinders. Course 3 8-7 Surface Area of Prisms and Cylinders

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Vocabulary surface area lateral face lateral surface Insert Lesson Title Here Course 3 8-7 Surface Area of Prisms and Cylinders

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Course 3 8-7 Surface Area of Prisms and Cylinders Surface area is the sum of the areas of all surfaces of a figure. The lateral faces of a prism are parallelograms that connect the bases. The lateral surface of a cylinder is the curved surface.

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Course 3 8-7 Surface Area of Prisms and Cylinders

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Course 3 8-7 Surface Area of Prisms and Cylinders A. S = 2r 2 + 2rh = 2(4 2 ) + 2(4)(6) = 80 in 2 251.2 in 2 B. S = 2B + Ph = 204 ft 2 = 2( 8 3) + (18)(10) 1212 Additional Example 1: Finding Surface Area Find the surface area of each figure to the nearest tenth. Use 3.14 for .

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Course 3 8-7 Surface Area of Prisms and Cylinders A. S = 2r 2 + 2rh = 2(15 2 ) + 2(15)(3) = 540 in 2 1695.6 cm 2 B. S = 2B + Ph = 252 cm 2 = 2( 7 6) + (21)(10) 1212 Check It Out: Example 1 15 cm 3 cm 7 cm 10 cm 6 cm Find the surface area of each figure to the nearest tenth. Use 3.14 for .

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Course 3 8-7 Surface Area of Prisms and Cylinders Additional Example 2: Exploring the Effects of Changing Dimensions A cylinder has diameter 8 in. and height 3 in. Explain whether tripling the 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.

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Course 3 8-7 Surface Area of Prisms and Cylinders Check It Out: Example 2 Original DimensionsDouble the HeightDouble the Radius S = 2r² + 2rh = 2(3) 2 + 2(3)(2) = 30in 2 ≈ 94.2 in 2 S = 2r 2 + 2r(2h) = 2(3) 2 + 2(3)(4) = 42in 2 ≈ 131.88 in 2 S = 2r 2 + 2(2r)h = 2(6) 2 + 2(3)(2) = 84in 2 ≈ 263.76 in 2 A cylinder has diameter 6 in. and height 2 in. Explain whether doubling the height would have the same effect on the surface area as doubling the radius. They would not have the same effect. Doubling the radius would increase the surface area more than doubling the height.

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Course 3 8-7 Surface Area of Prisms and Cylinders Additional Example 3: Application A cylindrical soup can is 7.6 cm in diameter and 11.2 cm tall. What is the area of the label that covers the side of the can? Only the lateral surface needs to be covered. Diameter = 7.6 cm, so r = 3.8 cm. L = 2rh = 2(3.8)(11.2) ≈ 267.3 cm 2

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Course 3 8-7 Surface Area of Prisms and Cylinders Check It Out: Example 3 A cylindrical storage tank that is 6 ft in diameter and 12 ft tall needs to be painted. The paint will cover 100 square feet per gallon. How many gallons will it take to paint the tank? The diameter is 6 ft, so r = 3 ft. S = 2r 2 + 2rh = 2(3 2 ) + 2(3)(12) ≈ 282.6 ft 2 Move the decimal point 2 places to the left to divide by 100. ≈ 2.826 gal

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3. All outer surfaces of a box are covered with gold foil, except the bottom. The box measures 6 in. long, 4 in. wide, and 3 in. high. How much gold foil was used? Lesson Quiz Find the surface area of each figure to the nearest tenth. Use 3.14 for . 1. the triangular prism 2. the cylinder 320.3 in 2 360 cm 2 Insert Lesson Title Here 84 in 2 Course 3 8-7 Surface Area of Prisms and Cylinders

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