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Holt CA Course 1 10-8 Volume of Prisms MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. Also covered: AF3.1, AF3.2 California Standards

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Holt CA Course 1 10-8 Volume of Prisms Vocabulary Volume Volume of Prisms Formula

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Holt CA Course 1 10-8 Volume of Prisms Volume is the number of cubic units needed to fill a space.

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Holt CA Course 1 10-8 Volume of Prisms You need 10, or 5 · 2, centimeter cubes to cover the bottom of this rectangular prism. You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes.

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Holt CA Course 1 10-8 Volume of Prisms Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cubic centimeters, or 30 cm 3.

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Holt CA Course 1 10-8 Volume of Prisms The volume of a rectangular prism is the area of its base times its height. This formula can be used to find the volume of any prism.

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. B = 26 · 11 The base is a rectangle. Multiply.B = 286 13 in. 26 in. 11 in. Step 1: Find the area of the base.

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 1 Continued: Find the volume of the rectangular prism. V = Bh Write the formula. V = 286 13Substitute for B and h. Multiply.V = 3,718 in 3 13 in. 26 in. 11 in. Step 2: Find the volume. The volume of the prism is 3,718 in 3.

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Holt CA Course 1 10-8 Volume of Prisms Student Practice 1: Find the volume of the rectangular prism. B = 29 · 12 The base is a rectangle. Multiply.B = 348 Step 1: Find the area of the base. 16 in. 29 in. 12 in.

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Holt CA Course 1 10-8 Volume of Prisms Student Practice 1 Continued: Find the volume of the rectangular prism. V = Bh Write the formula. V = 348 16Substitute for B and h. Multiply.V = 5,568 in 3 Step 2: Find the volume. The volume of the prism is 5,568 in 3. 16 in. 29 in. 12 in.

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Holt CA Course 1 10-8 Volume of Prisms You can also use the formula V= Bh to find the volume of a triangular prism. For triangular prisms, B represents the area of a triangle, rather than a rectangle.

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 2: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. A. Step 1: Find the area of the base. The base is a triangle. B = ( 3.9 1.3) 1 2 __ Multiply.B = 2.535

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 2A: Finding the Volume of a Triangular Prism Continued Find the volume of each triangular prism. A. Step 2: Find the volume. V = BhWrite the formula. V = 2.535 4 Substitute for B and h. Multiply.V = 10.14 m 3 The volume of the prism is 10.14 m 3.

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Holt CA Course 1 10-8 Volume of Prisms The height of a prism is the distance between its two bases. Caution!

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 2B: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. B. Step 1: Find the area of the base. The base is a triangle. B = ( 6.5 7) 1 2 __ Multiply.B = 22.75

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 2B: Finding the Volume of a Triangular Prism Continued Find the volume of each triangular prism. B. Step 2: Find the volume. V = BhWrite the formula. V = 22.75 6 Substitute for B and h. Multiply.V = 136.5 ft 3 The volume of the prism is 136.5 ft 3.

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Holt CA Course 1 10-8 Volume of Prisms Student Practice 2A: Find the volume of each triangular prism. A. Step 1: Find the area of the base. The base is a triangle. B = ( 4.2 1.6) 1 2 __ Multiply.B = 3.36 1.6 m 7 m 4.2 m

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Holt CA Course 1 10-8 Volume of Prisms Student Practice 2A Continued: Find the volume of each triangular prism. A. Step 2: Find the volume. V = BhWrite the formula. V = 3.36 7 Substitute for B and h. Multiply.V = 23.52 m 3 The volume of the prism is 23.52 m 3. 1.6 m 7 m 4.2 m

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Holt CA Course 1 10-8 Volume of Prisms Student Practice 2B: Find the volume of each triangular prism. B. Step 1: Find the area of the base. The base is a triangle. B = ( 4.5 9) 1 2 __ Multiply.B = 20.25 4.5 ft 5 ft 9 ft

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Holt CA Course 1 10-8 Volume of Prisms Student Practice 2B Continued: Find the volume of each triangular prism. B. Step 2: Find the volume. V = BhWrite the formula. V = 20.25 5 Substitute for B and h. Multiply.V = 101.25 ft 3 The volume of the prism is 101.25 ft 3. 4.5 ft 5 ft 9 ft

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 3: Application An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain. Step 1: Find the area of the base. The base is a triangle. B = 6 5.2 = 15.6 1 2 __ 5.2 cm 6 cm 3 cm

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Holt CA Course 1 10-8 Volume of Prisms Teacher Example 3 Continued An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain. Step 2: Find the volume. 5.2 cm 6 cm 3 cm V = BhWrite the formula. V = 15.6 3 = 46.8 cm 3 Substitute for B and h. No; each paperweight will require about 47 cm 3 of glass.

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Holt CA Course 1 10-8 Volume of Prisms Student Practice 3: An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain. Step 1: Find the area of the base. The base is a triangle. B = 6 5.5 = 16.5 1 2 __ 5.5 cm 6 cm 5 cm

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Holt CA Course 1 10-8 Volume of Prisms Step 2: Find the volume. V = BhWrite the formula. V = 16.5 5 = 82.5 cm 3 Substitute for B and h. No; each building will require about 83 cm 3 of paper. 5.5 cm 6 cm 5 cm Student Practice 3 Continued: An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain.

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Holt CA Course 1 10-8 Volume of Prisms 10.8 Warm-Up Find the volume of each figure. 1. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm 2. Find the volume of the figure shown.

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