Question

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





Remember to use the π
symbol on your Desmos calculator.


(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 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.

Given the radius \( r = 13 \) inches and the height \( h = 27 \) inches, we can substitute these values into the formula:

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

Calculating \( (13)^2 \):

\[
(13)^2 = 169
\]

Now substitute this into the equation:

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

Now calculating \( 169 \times 27 \):

\[
169 \times 27 = 4563
\]

Now substitute back into the volume equation:

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

Calculating \( \frac{1}{3} \times 4563 \):

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

So, we have:

\[
V = 1521 \pi
\]

Using \( \pi \approx 3.14159 \) to find the approximate volume:

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

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

The correct response is:

**4778.36 cubic inches**