10.2.5 Spheres (continued)
The volume of a sphere is determined in this example. The surface area of the sphere is given. To obtain the volume, substitute the value for the surface area into the formula for the surface area of a sphere and solve for the radius. The radius of the sphere is 7. Substitute the radius into the formula for the volume of a sphere. The volume is (1,372/3) π m 3 . The surface area of a sphere is determined in this example. The area of the great circle of the sphere is given. Substitute the area of the great circle into the formula for the area of a circle and solve for the radius. This is the radius of the sphere. Substitute the radius into the formula for the surface area of a sphere. The surface area is 144 π in 2 .
Example 4 Exploring Effects of Changing Dimensions
The effect of a change in dimension on the volume of a sphere is examined in this example. The radius of a sphere is given as 15 m. The volume of the sphere, obtained by substituting the radius into the formula for the volume of a sphere, is 4500 π m 3 . To form the second sphere, the radius length is multiplied by 2. The volume of the second sphere is 36,000 π m 3 . The volume of the second sphere is 2 3 = 8 times larger than the original volume. The volume of a sphere changes by the cube of the factor that the radius changes.
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