Question

Find the volume of a right circular cone that has a height of 11.8 ft and a base with a radius of 7.3 ft. Round your answer to the nearest tenth of a cubic foot.
Answer
Attempt 1 out of 2

Answer 1

To find the volume of a right circular cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.

Given:
- Height \( h = 11.8 \) ft,
- Radius \( r = 7.3 \) ft.

Now, plug in the values into the formula:

\[
V = \frac{1}{3} \pi (7.3)^2 (11.8)
\]

First, calculate \( (7.3)^2 \):

\[
(7.3)^2 = 53.29
\]

Now plug this value back into the volume formula:

\[
V = \frac{1}{3} \pi (53.29)(11.8)
\]

Now calculate \( 53.29 \times 11.8 \):

\[
53.29 \times 11.8 = 629.822
\]

Now plug this back into the volume formula:

\[
V = \frac{1}{3} \pi (629.822)
\]

Now divide \( 629.822 \) by 3:

\[
\frac{629.822}{3} \approx 209.94067
\]

Now multiply this by \( \pi \):

\[
V \approx 209.94067 \times 3.14159 \approx 659.584
\]

Lastly, round the volume to the nearest tenth:

\[
V \approx 659.6 \text{ cubic feet}
\]

Thus, the volume of the right circular cone is approximately **659.6 cubic feet**.