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Lesson Menu Five-Minute Check (over Lesson 12–4) CCSS Then/Now Key Concept: Volume of a Pyramid Example 1:Volume of a Pyramid Key Concept: Volume of a Cone Example 2:Volume of a Cone Example 3:Real-World Example: Find Real-World Volumes Concept Summary: Volumes of Solids

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Over Lesson 12–4 5-Minute Check 1 A.240 in 3 B.200 in 3 C.120 in 3 D.100 in 3 Find the volume of the prism. Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 1 A.240 in 3 B.200 in 3 C.120 in 3 D.100 in 3 Find the volume of the prism. Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 2 A.785.4 cm 3 B.547.3 cm 3 C.314.2 cm 3 D.157.1 cm 3 Find the volume of the cylinder. Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 2 A.785.4 cm 3 B.547.3 cm 3 C.314.2 cm 3 D.157.1 cm 3 Find the volume of the cylinder. Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 3 A.627.5 m 3 B.843.4 m 3 C.986.4 m 3 D.1017.9 m 3 What is the volume of the cylinder. Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 3 A.627.5 m 3 B.843.4 m 3 C.986.4 m 3 D.1017.9 m 3 What is the volume of the cylinder. Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 4 A.225.4 ft 3 B.203.7 ft 3 C.183.8 ft 3 D.152.8 ft 3 What is the volume of the prism? Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 4 A.225.4 ft 3 B.203.7 ft 3 C.183.8 ft 3 D.152.8 ft 3 What is the volume of the prism? Round to the nearest tenth if necessary.

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Over Lesson 12–4 5-Minute Check 5 A.1110 yd 3 B.1227 yd 3 C.1512 yd 3 D.2012 yd 3 Find the volume of a rectangular prism with a length of 12 yards, a width of 14 yards, and a height of 9 yards.

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Over Lesson 12–4 5-Minute Check 5 A.1110 yd 3 B.1227 yd 3 C.1512 yd 3 D.2012 yd 3 Find the volume of a rectangular prism with a length of 12 yards, a width of 14 yards, and a height of 9 yards.

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Over Lesson 12–4 5-Minute Check 6 A.65.5 ft 2 B.131 ft 2 C.650 ft 2 D.660 ft 2 The volume of a triangular prism is 655 cubic feet. The height of the prism is 5 feet. Find the area of one triangular base.

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Over Lesson 12–4 5-Minute Check 6 A.65.5 ft 2 B.131 ft 2 C.650 ft 2 D.660 ft 2 The volume of a triangular prism is 655 cubic feet. The height of the prism is 5 feet. Find the area of one triangular base.

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CCSS Content Standards G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Mathematical Practices 1 Make sense of problems and persevere in solving them. 7 Look for and make use of structure.

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Then/Now You found surface areas of pyramids and cones. Find volumes of pyramids. Find volumes of cones.

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Concept

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Example 1 Volume of a Pyramid Find the volume of the square pyramid. Answer: Volume of a pyramid Multiply. 21 s 3, h 7

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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. Volume of a pyramid Multiply. 21 s 3, h 7

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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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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 2A Volume of a Cone Answer: Use a calculator. Volume of a cone r = 9.1, h = 25 ≈ 2168.0

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Example 2A Volume of a Cone Answer: The volume of the cone is approximately 2168.0 cubic feet. Use a calculator. Volume of a cone r = 9.1, h = 25 ≈ 2168.0

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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 2B Volume of a Cone Answer: Use a calculator. Volume of a cone r = 5, h = 12 ≈ 314.2

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Example 2B Volume of a Cone Answer: The volume of the cone is approximately 314.2 cubic inches. Use a calculator. Volume of a cone r = 5, h = 12 ≈ 314.2

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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 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 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. Volume of a pyramid Answer: B = 36 ● 36, h = 52.5 Simplify.

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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. Volume of a pyramid Answer: The volume of the pyramidion is 22,680 cubic centimeters. B = 36 ● 36, h = 52.5 Simplify.

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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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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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End of the Lesson

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