10.1.1 Surface Area of Prisms and Cylinders (continued) Example 3 Finding Surface Areas of Composite Three-Dimensional Figures The surface area of a composite figure, a
rectangular prism with a missing volume the shape of a right cylinder, is determined in this example. The radius of the cylinder, the height of the prism (and cylinder), and the length and width of the prism base are given. The lateral area of the rectangular prism is obtained by substituting the known values for base dimensions and height into the formula. The area is 1440 cm 2 . The lateral area of the cylinder is found by substituting the known values for the radius and height into the formula. The area is 240 π cm 2 . The area of the bases of the figure are equal to the area of the prism base minus the area of the cylinder base. These are obtained by substituting the known values into the formulas for each. The area is 200 − 25 π cm 2 . The surface area is the sum of the lateral areas plus twice the base area. Using a calculator, the area is found to be approximately 2437 cm 2 .
Example 4 Exploring Effects of Changing Dimensions
The effect of a proportional doubling of the dimensions of a rectangular prism on the surface area of the prism are demonstrated in this example. The original dimensions of the rectangular prism are 2, 4, and 5 inches. The surface area of this prism is obtained by substituting the given values into the formula for surface area. The area is 76 in 2 . Doubling the dimensions proportionately gives dimensions of a new rectangular prism of 4, 8, and 10 inches. The new area of the prism is 304 in 2 . The new surface area is 2 2 times the surface area of the original prism, so the surface area changes by a factor of the proportional increase squared.
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