Question

A cone with radius
6
6 feet and height
15
15 feet is shown.
​
With a radus of 6 and hight of 15
Enter the volume, in cubic feet of the cone. Round your answer to the nearest hundredth

Answer 1

To calculate the volume of a cone, you can use the formula:

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

Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately \( 3.14159 \).

Given:
- \( r = 6 \) feet
- \( h = 15 \) feet

Now, substitute the values into the formula:

\[
V = \frac{1}{3} \pi (6)^2 (15)
\]

First, calculate \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substitute back into the formula:

\[
V = \frac{1}{3} \pi (36)(15)
\]

Now calculate \( 36 \times 15 \):

\[
36 \times 15 = 540
\]

Now substitute that value back:

\[
V = \frac{1}{3} \pi (540)
\]

Now divide \( 540 \) by \( 3 \):

\[
\frac{540}{3} = 180
\]

So the volume is:

\[
V = 180 \pi
\]

Now, substitute \( \pi \) with \( 3.14159 \):

\[
V \approx 180 \times 3.14159 \approx 565.486
\]

Finally, round to the nearest hundredth:

\[
V \approx 565.49
\]

Thus, the volume of the cone is approximately **565.49 cubic feet**.