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11.5 Volumes of Prisms and Cylinders OBJ: SWBAT find volumes of prisms and cylinders, use the formula for density, and use volumes of prisms and cylinders.
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Volume The number of cubic units contained in its interior. Formula: V = Bh
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Example 1: Find the volume of each prism.
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Example 2: Find the volume of each prism.
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Volume of a Cylinder Formula: V= Bh = πr²h
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Example 3: Find the volume of each cylinder.
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Density The amount of matter that an object has in a given unit of volume Formula: Density =
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Example 4 The diagram shows the dimensions of a standard gold bar at Fort Knox. Gold has a density of 19.3 grams per cubic centimeter. Find the mass of a standard gold bar to the nearest gram.
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Example 5 The diagram shows the dimensions of a concrete cylinder. Concrete has a density of 2.3 grams per cubic centimeter. Find the mass of the concrete cylinder to the nearest gram.
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Example 6 You are building a rectangular chest. You want the length to be 6 feet, the width to be 4 feet, and the volume to be 72 cubic feet. What should the height be?
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Example 7 You are building a 6-foot-tall dresser. You want the volume to be 36 cubic feet. What should the area of the base be? Give a possible length and width.
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Similar Solids Two solids of the same type with equal ratios of corresponding linear measures (i.e. heights, radii) Scale factor: ratio of the corresponding linear measures. Given a scale factor of k, then the ratio of their volumes is k³.
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Example 8: Find the corresponding volume.
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Example 9: Find the volume of the concrete block.
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