McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
6. Surface Areas and Volumes of Spheres
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Exercise 9 Page 852

Use the formula for the circumference of a circle to find its radius.

About 277.59 cubic inches

Practice makes perfect

A basketball used in professional games can be modeled by the following sphere.

Let r denote its radius. We know that the circumference of the ball is 29.5 inches. We are asked to find its surface area. First, let's find r using the formula for the circumference of a circle.
C=2π r
29.5=2π r
Solve for r
2π r=29.5
r=29.5/2π
r=4.69507082...
r≈ 4.70
Therefore, the radius of the sphere is about r=4.7 inches. Now, let's use the formula for the surface area of a sphere.
S=4π r^2
Substitute 4.7 for r and evaluate
S=4π ( 4.7)^2
S=4π(22.09)
S=88.36π
S=277.5911268...
S=277.59
Finally, we find that the surface area of the professional basketball is about 277.59 cubic inches.