Question

Can you please help me out with a question

Answer 1

In order to calculate the volume of the shaded portion, we shall take the following steps;

`\begin{gathered} \text{Volume of cylinder-Volume of spheres} \\ For\text{ the cylinder;} \\ \text{Vol}=\pi* r^2* h \\ r=6,h=25 \\ \text{Vol}=\pi*6^2*25 \\ \text{Vol}=\pi*36*25 \\ \text{Vol}=900\pi \\ \text{For the sphere;} \\ \text{Vol}=(4)/(3)\pi* r^3 \\ \text{For two spheres, we shall now have,} \\ \text{Vol}=2*(4)/(3)*\pi*6^3 \\ \text{Vol}=(8)/(3)*216*\pi \\ \text{Vol}=576\pi \end{gathered}`

Therefore, the volume of the shaded portion is derived as follows;

`\begin{gathered} \text{Vol}=900\pi-576\pi \\ \text{Vol}=324\pi in^3 \end{gathered}`

The answer is 324 pi cubic inches