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Mathematics

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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 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.

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rani01654 rani01654

Today at 2:19 PM

Answer:

2141.76 cubic inches

Step-by-step explanation:

Given that it measures 8.8 inches across a properly inflated basketball i.e. the diameter of each basketball is 8.8 inches.

So, the radius of the spherical ball is [tex]\frac{8.8}{2} =4.4[/tex] inches.

Now, a spherical solid has a volume given by [tex]\frac{4}{3} \pi r^{3}[/tex].

Hence, volume of air in side each basketball is = [tex]\frac{4}{3} \times \frac{22}{7}\times 4.4^{3} = 356.96[/tex] cubic inches.

Therefore, the total volume of air inside six balls will be = 6 × 356.96 = 2141.76 cubic inches. (Answer)

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