Question

a volleyball of radius 13 inches fits exactly in a cylinder with the same radius. inside the container there is empty space not taken up by the volleyball. what is the volume of that empty space? use 3.14 for π and round the answer to the nearest cubic inch. 3,067 in.³ 4,599 in.³ 13,797 in.³ 22,995 in.³

Explanation:

Step1: Calculate cylinder volume

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 13$ inches and $h=26$ inches. So $V_{cylinder}=3.14\times13^{2}\times26=3.14\times169\times26 = 13797.24$ cubic - inches.

Step2: Calculate volleyball (sphere) volume

The formula for the volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. With $r = 13$ inches, $V_{sphere}=\frac{4}{3}\times3.14\times13^{3}=\frac{4}{3}\times3.14\times2197\approx9198.11$ cubic - inches.

Step3: Calculate empty - space volume

The volume of the empty space $V = V_{cylinder}-V_{sphere}$. So $V=13797.24 - 9198.11=4599.13\approx4599$ cubic - inches.

Answer:

4,599 in.$^{3}$