Answer:
[tex]134.041\ \text{in}^3[/tex]
Step-by-step explanation:
r = Radius of sphere = Radius of basketball = 4 inches
h = Height of cylinder = 8 inches
Volume of unoccupied space will be the difference in volume between the cylinder and the basketball
[tex]\Delta V=\pi r^2h-\dfrac{4}{3}\pi r^3\\\Rightarrow \Delta V=\pi r^2(h-\dfrac{4}{3}r)\\\Rightarrow \Delta V=\pi\times 4^2(8-\dfrac{4}{3}\times 4)\\\Rightarrow \Delta V=134.041\ \text{in}^3[/tex]
Unoccupied volume in the container is [tex]134.041\ \text{in}^3[/tex].
