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Chapter 12 12.4 Volume of Prisms and Cylinders

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Volume of a Solid The number of cubic units contained in the solid Measured in cubic units such as m 3 (cubic meters) Surface Area and Volume

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Volume Postulates Postulate 27: Volume of a Cube –The volume of a cube is the the cube of the length of its side, or V = s 3 Postulate 28: Volume Congruence Postulate –If two polyhedra are congruent, then they have the same Volume Postulate 29: Volume Addition Postulate –The volume of a solid is the sum of the volumes of all its nonoverlapping parts

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Cavalieri’s Principle If two solids have the same height and the same cross-sectional area at every level, then they have the same volume The same thin slabs approximate the volume of both a centered square-based pyramid and a pyramid with the same base and its top over one corner. Cavalieri's Principle

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Volume of a Right Prism Theorem 12.7: Volume of a Prism –The volume V of a prism is V = Bh, where B is the area of the base and h is the height. 1.Area of Base: A = 9 3 Base is an equilateral triangle 2.Height: h = 4 Distance between bases 3.Volume: V = (9 3)4 = 36 3 m 3

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Find the Volume of the Right Prism 1.Base is a rectangle B = 5(4) 2.Height h = 12 3.Volume V = 20(12) = 240 cm 3

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Find the volume of the following right prisms B = 13(5) h = 8 V = 65(8) = 520 ft 3 B = ½(8)(8) = 32 h = 3 V = (32)3 96 = cm 3 B = h = 4 V = in 3

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Find the volume of the following right prisms 1.Base is a hexagon with side length 7 2.V = 1.Base is a square: B = 6 2 = 36 2.h = 15 3.V = 36(15) = 540 in 3

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Homework #64 Pg 746-748 10-15, 19-21, 25, 27, 35-38

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