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Lesson Menu Five-Minute Check (over Lesson 12–4) Then/Now New Vocabulary Key Concept: Lateral and Surface Area of Prisms Example 1:Surface Area of Prisms Example 2:Real-World Example: Surface Area of Prisms

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Over Lesson 12–4 5-Minute Check 1 A.324 in 3 B.224 in 3 C.162 in 3 D.108 in 3 Find the volume of the figure.

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Over Lesson 12–4 5-Minute Check 2 A.1003.6 cm 3 B.923.6 cm 3 C.378.7 cm 3 D.126 cm 3 Find the volume of the figure.

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Over Lesson 12–4 5-Minute Check 3 A.22.4 in 3 B.20.6 in 3 C.9.42 in 3 D.7.23 in 3 Find the volume of a sphere with a radius of 1.75 inches.

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Over Lesson 12–4 5-Minute Check 4 A.1080 mm 3 B.960 mm 3 C.360 mm 3 D.280 mm 3 Find the volume of a hexagonal pyramid with a base area of 120 mm 2 and height of 9 mm.

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Over Lesson 12–4 5-Minute Check 5 A.8.5 in 3 B. 7.5 in 3 C.6.5 in 3 D.5.5 in 3 What is the volume of a cone with a radius of 1.2 inches and a height of 5 inches?

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Over Lesson 12–4 5-Minute Check 6 A.48 centimeters B.24 centimeters C.36 centimeters D.12 centimeters A sphere and a cone have the same volume. Both have a radius of 12 centimeters. What is the approximate height of the cone?

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Then/Now You have already found the area of two-dimensional figures. (Lesson 11–6) Find lateral area and surface area of prisms. Find surface area of real-world objects shaped like prisms.

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Vocabulary lateral face lateral area surface area

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Concept

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Example 1 A Surface Area of Prisms A. Find the lateral and surface areas of the prism. Find the lateral area. L =Ph =(2 + 2w)(h) =(2 34 + 2 21)(4) =440 cm 2 Answer: The lateral area is 440 square centimeters. The surface area is 1868 square centimeters. Find the surface area. S =L + 2B =L + 2w =440 + 2(34)(21) =1868 cm 2

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Example 1 B Surface Area of Prisms B. Find the lateral and surface areas of the prism. L =PhWrite the formula. =(12 + 16 + 20)(3)P is perimeter of the triangular base. h is the height of the prism. =48 3 or 144 m 2 Simplify. The lateral area is made up of faces that are not parallel.

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Example 1 B Surface Area of Prisms Find the surface area. Answer: The lateral area of the triangular prism is 144 square meters. The surface area of the triangular prism is 336 square meters. S =L + 2BWrite the formula. =144 + 192 or 336 m 2 Simplify. Substitution

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Example 1 CYPA A. Find the lateral area and the surface area of the rectangular prism. A.lateral area, 152 in 2 ; surface area, 292 in 2 B.lateral area, 182 in 2 ; surface area, 322 in 2 C.lateral area, 304 in 2 ; surface area, 444 in 2 D.lateral area, 364 in 2 ; surface area, 560 in 2

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Example 1 CYPB B. Find the lateral area and the surface area of the triangular prism. A.lateral area, 19 ft 2 ; surface area, 31 ft 2 B.lateral area, 61 ft 2 ; surface area, 96 ft 2 C.lateral area, 84 ft 2 ; surface area, 96 ft 2 D.lateral area, 96 ft 2 ; surface area, 108 ft 2

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Example 2 Surface Area of Prisms CARPENTRY Alex is building a large storage box out of plywood. The box is a rectangular prism measuring 5 feet long, 3 feet wide, and 2 feet high. Find the number of sheets of plywood he would need to buy to build the box if 1 sheet covers 32 square feet. Find the lateral area. L = Ph = (2 + 2w)h = (2 5 + 2 3)2 = 32 ft 2 Find the surface area. S = L + 2B = L + 2w = 32 + 2 3 5 = 32 + 30 or 62 ft 2

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Example 2 Surface Area of Prisms One sheet of plywood covers 32 ft 2 and two sheets cover 2 32 or 64 ft 2. 32 < 62 < 64 Answer: Alex will need at least 2 sheets of plywood.

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Example 2 CYP A.1 quart B.2 quarts C.3 quarts D.4 quarts Jan is painting all the sides of a rectangular cabinet. The cabinet measures 3 feet long, 4 feet wide, and 5 feet tall. How much paint will she need if one quart of paint covers 50 square feet?

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