Question

Jake volunteers to help out his younger brother's 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 Jake’s basketballs? Assume that the wall of each ball is infinitely thin. A. 681. 47 cubic inches B. 1,651. 32 cubic inches C. 3,775. 23 cubic inches D. 5,451. 78 cubic inches.

Answer 1

The total volume of air inside six of Jake's basketballs is 2140.9074 in³.

volume of sphere

volume of sphere = $\dfrac{4}{3} \times\pi\times radius^3$

Given to us,

properly inflated basketball measures = 8.8 inches across

so, the diameter of each basketball, d = 8.8 inches,

Also, the radius of each basketball, r = 4.4 inches,

Assumption has given, that the wall of each ball is infinitely thin.

As we know a basketball is a sphere in shape, thus,

$\begin{aligned}Volume &= \dfrac{4}{3} \times\pi\times radius^3\\&= \dfrac{4}{3} \times\pi\times 4.4^3\\&= 356.8179\ in^3\\\end{aligned}$

A Total volume of air inside six of Jake's basketballs =volume of 1 basketball x 6

$\begin{aligned}Volume\ of\ six\ basketball &= 356.81790\times6\\&=2,140.9074\ in^3\end{aligned}$

Hence, the total volume of air inside six of Jake's basketballs is 2140.9074 in³.

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