In order to calculate the volume of the shaded portion, we shall take the following steps;
[tex]\begin{gathered} \text{Volume of cylinder-Volume of spheres} \\ For\text{ the cylinder;} \\ \text{Vol}=\pi\times r^2\times h \\ r=6,h=25 \\ \text{Vol}=\pi\times6^2\times25 \\ \text{Vol}=\pi\times36\times25 \\ \text{Vol}=900\pi \\ \text{For the sphere;} \\ \text{Vol}=\frac{4}{3}\pi\times r^3 \\ \text{For two spheres, we shall now have,} \\ \text{Vol}=2\times\frac{4}{3}\times\pi\times6^3 \\ \text{Vol}=\frac{8}{3}\times216\times\pi \\ \text{Vol}=576\pi \end{gathered}[/tex]Therefore, the volume of the shaded portion is derived as follows;
[tex]\begin{gathered} \text{Vol}=900\pi-576\pi \\ \text{Vol}=324\pi in^3 \end{gathered}[/tex]The answer is 324 pi cubic inches
