10.2.5 Spheres (continued)
Example 5 Finding Surface Areas and Volumes in Composite Figures
The volume of a composite solid is determined in this example. The solid is a right cylinder with a hemisphere on top of it. The radii of both the cylinder and the hemisphere are given as 3 cm. The height of the cylinder is given as 10 cm. To find the volume of the cylinder, substitute the radius and height into the formula for the volume of a cylinder. The volume is 90 π cm 3 . To find the volume of the hemisphere, substitute the radius into the formula for the volume of a sphere and divide the resulting volume by 2. The volume of the hemisphere is 18 π cm 3 . The combined volume is 108 π cm 3 . The surface area of a composite solid is determined in this example. The solid is a right cylinder with a hemisphere on top of it. The radii of both the cylinder and the hemisphere are given as 3 cm. The height of the cylinder is given as 10 cm. To find the surface area of the base of the cylinder, substitute the radius into the formula for the area of a circle. The area is 9 π cm 2 . To find the lateral surface area of the cylinder, substitute the¸ radius and height into the formula for the lateral area of a cylinder. The area is 60 π cm 2 . To find the surface area of the hemisphere, substitute the radius into the formula for the surface area of a sphere and divide the resulting area by 2. The surface area of the hemisphere is 18 π cm 2 . The combined surface area is 87 π cm 2 .
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