Key Objectives • Learn and apply the formula for the volume of a prism. • Learn and apply the formula for the volume of a cylinder. Key Terms • The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. Formulas • Volume of a Prism The volume of a prism with base area B and height h is V = Bh . • Volume of a Right Rectangular Prism The volume of a right rectangular prism with length l , width w , and height h is V = lwh . • Volume of a Cube The volume of a cube with edge length s is V = s 3 . • Volume of a Cylinder The volume of a cylinder with base area B , radius r , and height h is V = Bh , or V = πr 2 h . Example 1 Finding Volumes of Prisms 10.1.3 Volume of Prisms and Cylinders
The volume of a rectangular prism is determined in this example. The length, width, and height of the prism are given. To find the volume of the prism, substitute the given values into the formula for the volume of a rectangular prism. The volume is equal to 30 cm 3 . Notice that the units of volume are cubed.
The volume of a cube is determined in this example. The length of the edges of the cube are given. To find the volume of the cube, substitute the given value into the formula for the volume of a cube. The volume is 125 cm 3 .
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