Question

Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches.





(1 point)
Responses

4778.36 cubic inches
4778.36 cubic inches

176.98 cubic inches
176.98 cubic inches

14,335.09 cubic inches
14,335.09 cubic inches

1521 cubic inches

Answer 1

To calculate the volume \( V \) of a cone, you can use the formula:

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

where \( r \) is the radius and \( h \) is the height of the cone.

Given:
- \( r = 13 \) inches
- \( h = 27 \) inches

Now, substitute the values into the formula:

\[
V = \frac{1}{3} \pi (13^2)(27)
\]

Calculating \( 13^2 \):

\[
13^2 = 169
\]

Now substitute that into the volume formula:

\[
V = \frac{1}{3} \pi (169)(27)
\]

Calculating \( 169 \times 27 \):

\[
169 \times 27 = 4563
\]

Now substituting back into the volume formula:

\[
V = \frac{1}{3} \pi (4563)
\]

Calculating \( \frac{4563}{3} \):

\[
\frac{4563}{3} = 1521
\]

Now multiply by \( \pi \):

\[
V \approx 1521 \times 3.14159 \approx 4778.36 \text{ cubic inches}
\]

So the volume of the cone is approximately:

\[
\boxed{4778.36} \text{ cubic inches}
\]