[tex]\begin{gathered} Volume\text{ not occupied}=Box\text{ volume - }ball\text{ volume} \\ Boxvolume=l^3 \\ ball\text{ volume=}\frac{4}{3}\pi r^3 \\ From\text{ the given information} \\ l=8.5\text{ in} \\ r=\frac{8.5}{2}in\text{ =4.25in } \\ Boxvolume=(8.5)^3 \\ Boxvolume=614.13in^3 \\ ball\text{ volume=}\frac{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}[/tex]
