Question

Find the volume of the cylinder.
.
.
.
Question content area top right
Part 1
6 in.
8 in.
​(This figure is not to​ scale.)
Question content area bottom
Part 1
The volume of the cylinder is
  
enter your response here in.cubed.
​(Type an exact answer in terms of pi​.)

Answer 1

To find the volume of a cylinder, you can use the formula:

\[
V = \pi r^2 h
\]

where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cylinder.

From the information provided, you have:

- Diameter of the cylinder = 6 in.
- Height of the cylinder = 8 in.

First, we need to find the radius, which is half of the diameter:

\[
r = \frac{6 \text{ in}}{2} = 3 \text{ in}
\]

Now, we can substitute the radius and height into the volume formula:

\[
V = \pi (3 \text{ in})^2 (8 \text{ in})
\]

Calculating \( (3 \text{ in})^2 \):

\[
(3 \text{ in})^2 = 9 \text{ in}^2
\]

Now substitute back into the volume equation:

\[
V = \pi (9 \text{ in}^2) (8 \text{ in}) = 72\pi \text{ in}^3
\]

Thus, the volume of the cylinder is:

\[
\boxed{72\pi \text{ in}^3}
\]