Question

Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches.
1. 4778.36 cubic inches
2. 176.98 cubic inches
3. 14,335.09 cubic inches
4. 1521 cubic inches

Answer 1

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

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

where:
- \( r \) is the radius of the base of the cone
- \( h \) is the height of the cone
- \( \pi \) is approximately 3.14159

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

Plugging these values into the formula:

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

Calculating \( (13)^2 \):

\[
(13)^2 = 169
\]

Now substitute back into the volume formula:

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

Calculating \( 169 \times 27 \):

\[
169 \times 27 = 4563
\]

Now substitute this back into the volume formula:

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

Then, multiply by \( \frac{1}{3} \):

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

Now, multiplying by \( \pi \):

\[
V \approx 1521 \pi
\]

Using \( \pi \approx 3.14159 \):

\[
V \approx 1521 \times 3.14159 \approx 4778.36
\]

Thus, the volume of the cone is approximately \( 4778.36 \) cubic inches.

The correct answer is:

**1. 4778.36 cubic inches**