Question

A basketball with a diameter of approximately 8.5 inches is packed in a cube-shaped box sothat it touches each side of the interior of the box. What is the volume of the space in the boxnot occupied by the basketball? Round to the nearest tenth.

Answer 1

`\begin{gathered} Volume\text{ not occupied}=Box\text{ volume - }ball\text{ volume} \\ Boxvolume=l^3 \\ ball\text{ volume=}(4)/(3)\pi r^3 \\ From\text{ the given information} \\ l=8.5\text{ in} \\ r=(8.5)/(2)in\text{ =4.25in } \\ Boxvolume=(8.5)^3 \\ Boxvolume=614.13in^3 \\ ball\text{ volume=}(4)/(3)\pi(4.25)^3 \\ ball\text{ volume=321.56 in}^3 \\ Volume\text{ not occupied}=614.13in^3\text{ - 321.56 in}^3 \\ Volume\text{ not occupied}\approx292.6in^3 \\ \text{The space in the box not occupied by the basketball is }292.6in^3 \end{gathered}`