Question

If r = 12 units and x = 15 units, then what is the volume of the cylinder shown above?

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, and \( h \) is the height of the cylinder.

From your provided values:
- \( r = 12 \) units (which we'll use for the radius)
- \( h = 15 \) units (which we'll use for the height)

Now, substitute these values into the volume formula:

\[
V = \pi (12)^2 (15)
\]

Calculating \( (12)^2 \):

\[
(12)^2 = 144
\]

Now substitute that back into the volume formula:

\[
V = \pi (144) (15)
\]

Now calculate \( 144 \times 15 \):

\[
144 \times 15 = 2160
\]

Now substituting back into the formula gives:

\[
V = 2160\pi \text{ cubic units}
\]

So, the volume of the cylinder is:

\[
V \approx 6783.18 \text{ cubic units} \quad (\text{using } \pi \approx 3.14)
\]

Thus, the exact volume is:

\[
V = 2160\pi \text{ cubic units}
\]
and approximately \( 6783.18 \text{ cubic units} \) if you use the numerical approximation for \(\pi\).