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Chapter 12.4 and 12.5 Volume of Prisms, Cylinders, Pyramids, and Cones

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Volume Volume of a solid is the measure of the amount of space the solid encloses. Volume is measured in cubic units.

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Concept

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Example 1 Volume of a Prism Answer: The volume of the prism is 1500 cubic centimeters. Find the volume of the prism.

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Example 1 A.6480 in 3 B.8100 in 3 C.3240 in 3 D.4050 in 3 Find the volume of the prism.

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Concept

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Example 2 Volume of a Cylinder Find the volume of the cylinder to the nearest tenth. Answer: The volume is approximately 18.3 cm 3.

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Example 2 A.62.8 cm 3 B.628.3 cm 3 C.125.7 cm 3 D.1005.3 cm 3 Find the volume of the cylinder to the nearest tenth.

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Example 3 Volume of an Oblique Solid Find the volume of the oblique cylinder to the nearest tenth. Answer: The volume is approximately 17,671.5 cubic feet.

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Example 3 A.1520.5 cm 3 B.16,725.8 cm 3 C.5324 cm 3 D.8362.9 cm 3 Find the volume of the oblique cylinder to the nearest tenth.

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Example 4 Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A, what is the length of each prism? A12B8 C4D3.5 Prism APrism B Comparing Volumes of Solids

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Example 4 A.4 in. B.6 in. C.8 in. D.10.5 in. Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 192 cubic inches greater than the volume of Prism A, what is the length of each prism? Prism A Prism B

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Concept

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Example 1 Volume of a Pyramid Find the volume of the square pyramid. Answer: The volume of the pyramid is 21 cubic inches.

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Example 1 Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid. A.416 ft 3 B. C. D.

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Concept

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Example 2A Volume of a Cone A. Find the volume of the oblique cone to the nearest tenth.

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Example 2B Volume of a Cone B. Find the volume of the cone to the nearest tenth.

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Example 2A A.444.4 m 3 B.27,463.2 m 3 C.3051.5 m 3 D.9154.4 m 3 A. Find the volume of the oblique cone to the nearest tenth.

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Example 2B A.3015.9 m 3 B.125.7 m 3 C.1005.3 m 3 D.251.3 m 3 B. Find the volume of the cone to the nearest tenth.

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Example 3 Find Real-World Volumes SCULPTURE At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth. Answer: The volume of the pyramidion is 22,680 cubic centimeters.

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Example 3 A.18,775 cm 3 B.19,500 cm 3 C.20,050 cm 3 D.21,000 cm 3 SCULPTURE In a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

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Concept

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