Question

jake volunteers to help out his younger brothers basketball team in his free - time. one of his tasks is to ensure that all the basketballs have enough air in them. given that a properly inflated basketball measures 8.8 inches across, what is the total volume of air inside six of jakes basketballs? assume that the wall of each ball is infinitely thin.

a. 661.47π cubic inches

b. 1,561.32π cubic inches

c. 3,775.23π cubic inches

d. 5,451.75π cubic inches

Explanation:

Step1: Find the radius

The diameter is 8.8 inches, so the radius $r = \frac{8.8}{2}=4.4$ inches.

Step2: Calculate the volume of one basketball

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substituting $r = 4.4$, we get $V=\frac{4}{3}\pi(4.4)^{3}$.

Step3: Find the volume of six basketballs

$V_{total}=6\times\frac{4}{3}\pi(4.4)^{3}=32\pi(4.4)^{3}=3775.23\pi$ cubic - inches.

Answer:

C. 3,775.23 $\pi$ cubic inches