10.1.3 Volume of Prisms and Cylinders (continued)
Example 4 Exploring Effects of Changing Dimension
The effects of a proportional increase in dimensions on the volume of a cylinder is examined in this example. The radius of a right cylinder is given as 8 cm and its height is 20 cm. To calculate the volume of the cylinder, substitute the values for the radius and height into the formula for volume. The volume of the cylinder is 1280 π cm 3 . The new cylinder has dimensions that are half those of the original cylinder: the radius is 4 cm and the height is 10 cm. To calculate the volume, substitute the values into the formula for volume. The new volume is 160 π cm 3 . The new volume is one-eighth the original volume, or The change in volume is a cube of the factor by which the dimensions were changed. ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 . 1 3
Example 5 Finding Volumes of Composite Three-Dimensional Figures
The volume of a composite solid is determined in this example. The solid is a rectangular prism with a cylinder on top of it. The length, width, and height of the rectangular prism and the height of the cylinder are given. To calculate the volume of the prism, substitute the length, width, and height into the formula for the volume of a rectangular prism. The volume is 160 m 3 . To calculate the volume of the cylinder, first notice that the base of the cylinder is as wide as the base of the rectangular prism, meaning it has a diameter of 4 m and a radius of 2 m. Substitute the radius and the given height into the formula for the volume of a cylinder. The volume of the cylinder is 40 π m 3 . The volume of the composite solid is 160 + 40 π m 3 .
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