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Lesson Menu Five-Minute Check (over Lesson 12–3) CCSS Then/Now Key Concept : Volume of a Prism Example 1: Volume of a Prism Key Concept: Volume of a Cylinder Example 2: Volume of a Cylinder Key Concept: Cavalieri’s Principle Example 3: Volume of an Oblique Solid Example 4: Standardized Test Example: Comparing Volumes of Solids

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Over Lesson 12–3 5-Minute Check 1 A.600 in 2 B.623.2 in 2 C.635.3 in 2 D.647.4 in 2 Find the surface area of the regular pyramid.

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Over Lesson 12–3 5-Minute Check 1 A.600 in 2 B.623.2 in 2 C.635.3 in 2 D.647.4 in 2 Find the surface area of the regular pyramid.

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Over Lesson 12–3 5-Minute Check 2 A.628.3 ft 2 B.642.3 ft 2 C.677.8 ft 2 D.753.9 ft 2 Find the surface area of the cone.

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Over Lesson 12–3 5-Minute Check 2 A.628.3 ft 2 B.642.3 ft 2 C.677.8 ft 2 D.753.9 ft 2 Find the surface area of the cone.

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Over Lesson 12–3 5-Minute Check 3 A.420 ft 2 B.480 ft 2 C.679.8 ft 2 D.710 ft 2 Find the surface area of the regular pyramid.

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Over Lesson 12–3 5-Minute Check 3 A.420 ft 2 B.480 ft 2 C.679.8 ft 2 D.710 ft 2 Find the surface area of the regular pyramid.

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Over Lesson 12–3 5-Minute Check 4 A.214.2 m 2 B.221.0 m 2 C.233.4 m 2 D.247.5 m 2 Find the surface area of the cone.

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Over Lesson 12–3 5-Minute Check 4 A.214.2 m 2 B.221.0 m 2 C.233.4 m 2 D.247.5 m 2 Find the surface area of the cone.

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Over Lesson 12–3 5-Minute Check 5 A.80 ft 2 B.200 ft 2 C.240 ft 2 D.260 ft 2 Find the surface area of a square pyramid with base length of 10 feet and slant height of 8 feet.

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Over Lesson 12–3 5-Minute Check 5 A.80 ft 2 B.200 ft 2 C.240 ft 2 D.260 ft 2 Find the surface area of a square pyramid with base length of 10 feet and slant height of 8 feet.

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Over Lesson 12–3 5-Minute Check 6 A.204.2 cm 2 B.282.7 cm 2 C.408.4 cm 2 D.722.6 cm 2 Find the lateral area of a cone with a diameter length of 10 centimeters and a slant height of 13 centimeters. Round your answer to the nearest tenth.

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Over Lesson 12–3 5-Minute Check 6 A.204.2 cm 2 B.282.7 cm 2 C.408.4 cm 2 D.722.6 cm 2 Find the lateral area of a cone with a diameter length of 10 centimeters and a slant height of 13 centimeters. Round your answer to the nearest tenth.

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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 prisms and cylinders. Find volumes of prisms. Find volumes of cylinders.

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Concept

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Example 1 Volume of a Prism Answer: V BhVolume of a prism 1500Simplify. Find the volume of the prism.

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Example 1 Volume of a Prism Answer: The volume of the prism is 1500 cubic centimeters. V BhVolume of a prism 1500Simplify. 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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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: Volume of a cylinder ≈18.3Use a calculator. = (1.8) 2 (1.8)r = 1.8 and h = 1.8

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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. Volume of a cylinder ≈18.3Use a calculator. = (1.8) 2 (1.8)r = 1.8 and h = 1.8

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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 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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Concept

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Example 3 Volume of an Oblique Solid Find the volume of the oblique cylinder to the nearest tenth. To find the volume, use the formula for a right cylinder. Answer: Volume of a cylinder Use a calculator. r 15, h 25

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Example 3 Volume of an Oblique Solid Find the volume of the oblique cylinder to the nearest tenth. To find the volume, use the formula for a right cylinder. Answer: The volume is approximately 17,671.5 cubic feet. Volume of a cylinder Use a calculator. r 15, h 25

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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 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 Read the Test Item You know the volume of each solid and that the difference between their volumes is 128 cubic inches. Solve the Test Item Volume of Prism B – Volume of Prism A=128Write an equation. 4x ● 9 – 4x ● 5=128Use V = Bh. 16x=128Simplify. x=8Divide each side by 16. Answer: Comparing Volumes of Solids

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Example 4 Read the Test Item You know the volume of each solid and that the difference between their volumes is 128 cubic inches. Solve the Test Item Volume of Prism B – Volume of Prism A=128Write an equation. 4x ● 9 – 4x ● 5=128Use V = Bh. 16x=128Simplify. x=8Divide each side by 16. Answer: The length of each prism is 8 inches. The correct answer is 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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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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End of the Lesson

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