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. 681.47 π cubic inches b. 1,651.32 π cubic inches c. 3,775.23 π cubic inches d. 5,451.78 π cubic inches

Explanation:

Step1: Find the radius of the basketball

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

Step2: Use the volume - formula for a sphere

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 4.4$ into the formula: $V=\frac{4}{3}\pi(4.4)^{3}=\frac{4}{3}\pi\times85.184$.

Step3: Calculate the volume of one basketball

$V=\frac{4\times85.184}{3}\pi=\frac{340.736}{3}\pi\approx113.579\pi$ cubic inches.

Step4: Calculate the volume of six basketballs

Multiply the volume of one basketball by 6. $V_{total}=6\times113.579\pi = 681.47\pi$ cubic inches.

Answer:

A. 681.47 $\pi$ cubic inches