Question

how much air is inside an 24 - inch wide beach ball? leave your answer in terms of $pi$.

Explanation:

Step1: Find the radius

The diameter of the beach - ball is 24 inches. The radius $r$ of a sphere is half of its diameter. So, $r=\frac{24}{2}=12$ inches.

Step2: Use the volume formula for a sphere

The volume $V$ of a sphere is given by the formula $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 12$ into the formula: $V=\frac{4}{3}\pi\times(12)^{3}$.

Step3: Calculate $(12)^{3}$

$(12)^{3}=12\times12\times12 = 1728$. Then $V=\frac{4}{3}\pi\times1728$.

Step4: Multiply by $\frac{4}{3}$

$\frac{4}{3}\times1728 = 4\times576=2304$. So, $V = 2304\pi$ $in^{3}$.

Answer:

$2304$