Question

Find the volume of the composite solid. FYI: I’m trying to understanding what I’m doing. I just need some clarity on how to get volume of this figure.

Answer 1

Given:

• Radius = 2 in

,

• Height = 2 in

Let's find the volume of the composite figure.

To find the volume of this figure, we are to subtract the volume of hemisphere from the volume of the cylinder.

• Volume of Cylinder:

To find the volume of the cylinder, apply the formula:

$V=\pi r^2h$

Thus, we have:

$\begin{gathered} V=\pi *2^2*2 \\ \\ V=8\pi\text{ in}^3 \end{gathered}$

Now, to find the volume of the hemisphere, we have:

$\begin{gathered} V_h=\frac{1}{2}(\frac{4}{3}\pi r^3) \\ \\ V_h=\frac{1}{2}*\frac{4}{3}*\pi *2^3 \\ \\ V_h=\frac{1*4*2^3}{2*3}\pi \\ \\ V_h=\frac{32}{6}\pi\text{ in}^3=\frac{16}{3}\pi\text{ in}^3 \end{gathered}$

Now, to find the volume of the figure, let's subtract the volume of the hemisphere from the volume of the cylinder.

$\begin{gathered} V=8\pi-\frac{16}{3}\pi \\ \\ V=\frac{24\pi-16\pi}{3} \\ \\ V=\frac{8}{3}\pi\text{ in}^3 \end{gathered}$

Therefore, the volume of the figure is:

$\frac{8}{3}\pi\text{ in}^3\approx8.38\text{ in}^3$

ANSWER:

$8.38\text{ in}^3$