Question

A cylinder has radius 6 feet and height 10 feet. Find the volume and select the correct units.

Answer 1

The formula for the volume \( V \) of a cylinder is given by:

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

where:
- \( r \) is the radius,
- \( h \) is the height.

For your cylinder, the radius \( r \) is 6 feet and the height \( h \) is 10 feet. Plugging in these values:

\[
V = \pi (6 \text{ ft})^2 (10 \text{ ft})
\]

First, calculate \( (6 \text{ ft})^2 \):

\[
(6 \text{ ft})^2 = 36 \text{ ft}^2
\]

Now substitute this back into the volume formula:

\[
V = \pi (36 \text{ ft}^2) (10 \text{ ft}) = 360 \pi \text{ ft}^3
\]

Now, using the approximation \( \pi \approx 3.14 \):

\[
360 \pi \text{ ft}^3 \approx 360 \times 3.14 \text{ ft}^3 \approx 1134.4 \text{ ft}^3
\]

Thus, the volume of the cylinder is approximately \( 1134.4 \text{ ft}^3 \).

In conclusion, the volume of the cylinder is:

\[
\boxed{360\pi \text{ ft}^3} \quad \text{or approximately} \quad \boxed{1134.4 \text{ ft}^3}
\]