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9-6 Volume of Prisms Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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9-6 Volume of Prisms Warm Up Find the area of each figure. Use 3.14 for . 96 in 2 50.24 ft 2 1. rectangle with base length 8 in. and height 12 in. 2. circle with diameter 8 ft

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9-6 Volume of Prisms Problem of the Day A rectangular park is bordered by a 3- foot-wide sidewalk. The park, including the sidewalk, measures 125 ft by 180 ft. What is the area of the park, not including the sidewalk? 20,706 ft 2 Volume of Prisms

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9-6 Volume of Prisms MA.6.G.4.3 Determine the missing dimension of a prism…given its volume…or the volume given the dimensions. Also MA.6.A.3.4 Sunshine State Standards

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9-6 Volume of Prisms Vocabulary volume

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9-6 Volume of Prisms Volume is the number of cubic units needed to fill a space.

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9-6 Volume of Prisms You need 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism. You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes. Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm 3.

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9-6 Volume of Prisms Additional Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. V = lwh Write the formula. V = 26 11 13l = 26; w = 11; h = 13 Multiply.V = 3,718 in 3

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9-6 Volume of Prisms Check It Out: Example 1A Find the volume of each rectangular prism. V = lwh = 2 × 3 × 8 = 48 ft 3

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9-6 Volume of Prisms Check It Out: Example 1B Find the volume of each rectangular prism. V = lwh = 1 × 1 × 2 = 2 km 3

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9-6 Volume of Prisms Check It Out: Example 1C Find the volume of each rectangular prism. V = lwh = 8.4 × 5.1 × 6 = 257.04 in 3

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9-6 Volume of Prisms To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height.

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9-6 Volume of Prisms Additional Example 2: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. V = BhWrite the formula. V = ( 3.9 1.3) 4 1 2 __ B = 3.9 1.3; h = 4. 1 2 __ Multiply.V = 10.14 m 3

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9-6 Volume of Prisms The bases of a prism are always two congruent, parallel polygons. Caution!

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9-6 Volume of Prisms Check It Out: Example 2A V = Bh (8)(7)12 = 336 ft 2 3 = 1

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9-6 Volume of Prisms Check It Out: Example 2B V = Bh = ( )(2)1 2 1 2 1 4 3 = 8 7 m 3 2 1 m

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9-6 Volume of Prisms Check It Out: Example 2C V = Bh = (3)(5.4)8.6 2 1 = 69.66 cm 3

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9-6 Volume of Prisms Additional Example 3: Problem Solving Application Suppose a facial tissue company ships 16 cubic tissue boxes in each case. What are the possible dimensions for a case of tissue boxes? 1 Understand the Problem The answer will be all possible dimensions for a case of 16 cubic boxes. List the important information: There are 16 tissue boxes in a case. The boxes are cubic, or square prisms.

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9-6 Volume of Prisms You can make models using cubes to find the possible dimensions for a case of 16 tissue boxes. 2 Make a Plan Additional Example 3 Continued

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9-6 Volume of Prisms Solve 3 You can make models using cubes to find the possible dimensions for a case of 16 cubes. Additional Example 3 Continued The possible dimensions for a case of 16 cubic tissue boxes are the following: 16 x 1 x 1, 8 x 2 x 1, 4 x 4 x 1, and 4 x 2 x 2.

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9-6 Volume of Prisms Notice that each dimension is a factor of 16. Also, the product of the dimensions (length width height) is 16, showing that the volume of each case is 16 cubes. Look Back 4 Additional Example 3 Continued

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9-6 Volume of Prisms Check It Out: Example 3 A toy box is a rectangular prism that is 3 ft long, 2 feet wide, and 2 feet tall. Another toy box has the same dimensions, except that it is longer. If the longer toy box has a volume that is 50% greater than the original toy box, what is the length of the longer toy box? The original volume is 3 × 2 × 2 = 12 ft. 50% of 12 is 6, so the longer toy box has a volume of 12 + 6 = 18 ft. So L × 2 × 2 = 18, and L = 18 ÷ 4 = 4.5. The length of the longer toy box is 4.5 feet. 3 3

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