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11.4 Volume of Prisms & Cylinders

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Exploring Volume The volume of a solid is the number of cubic units contained in its interior (inside). Volume is measured in cubic units, such as cubic meters (m 3 ).

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Ex. 1: Finding the Volume of a rectangular prism

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Finding Volumes of prisms and cylinders. Theorem 11.5 is named after Bonaventura Cavalieri (1598-1647).

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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.

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Volume Theorems 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. Volume of a Cylinder — The volume V of a cylinder is V=Bh= r 2 h, where B is the area of a base, h is the height, and r is the radius of the base.

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Ex. 2: Finding Volumes Find the volume of the right prism. V = BhVolume of a prism formula A = ½ bhArea of a triangle A = ½ (3)(4)Substitute values A = 6 cm 2 Multiply values -- base V = (6)(2) Substitute values V = 12 cm 3 Multiply values & solve

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Ex. 2: Finding Volumes Find the volume of the right cylinder. V = BhVolume of a prism formula A = r 2 Area of a circle A = 8 2 Substitute values A = 64 in. 2 Multiply values -- base V = 64 (6) Substitute values V = 384 in. 3 Multiply values & solve V = 1206.37 in. 3 Simplify

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Ex. 3: Using Volumes Use the measurements given to solve for x.

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Ex. 3: Using Volumes Use the measurements given to solve for x.

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