10.2.5 Spheres (continued)
The volume of a hemisphere is determined in this example. The radius of the hemisphere is given. To obtain the volume, substitute the radius length into the formula for the volume of a sphere. Multiply the volume obtained by 1/2. The volume of the hemisphere is (250/3) π m 3 .
Example 2 Sports Application
The volumes of two spheres are compared in this application example. The diameters of the two spheres are given. To calculate the volumes, first divide the diameters by two to obtain the radii. Substitute the radii into formulas for the volumes of the spheres. The basketball has a volume of about 449 in 3 . The baseball has a volume of about 33.5 in 3 . To find out how many more times larger the volume of the basketball is than the baseball, set up a ratio. Divide the values in the ratio to find the size factor. The basketball is about 13.4 times as voluminous as the baseball.
Example 3 Finding the Surface Area of Spheres
The surface area of a sphere is determined in this example. The diameter of the sphere is given. To obtain the surface area, divide the diameter by two and substitute the resulting radius length into the formula for the surface area of a sphere. The area is 25 π ft 2 .
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