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1 year ago

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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 b

asketballs 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 Jakeâ€™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.

1 answer:

Nataly [62]1 year ago

8 0

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

<h2 /><h2>volume of sphere</h2>

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

<h3>Given to us,</h3>

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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