Question

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

Answer 1

To find 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, and \( h \) is the height of the cone.

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

First, substitute the values into the formula:

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

Now calculate \( (13)^2 \):

\[
(13)^2 = 169
\]

Next, substitute \( 169 \) back into the volume formula:

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

Now calculate \( 169 \times 27 \):

\[
169 \times 27 = 4563
\]

Thus, we have:

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

Now divide \( 4563 \) by \( 3 \):

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

So the volume becomes:

\[
V = 1521 \pi
\]

Finally, if you want the volume in numerical form, you can use an approximation of \( \pi \approx 3.14 \):

\[
V \approx 1521 \times 3.14 \approx 4779.14 \text{ cubic inches}
\]

Thus, the volume of the cone is:

\[
\boxed{1521\pi} \text{ cubic inches} \quad (\approx 4779.14 \text{ cubic inches})
\]