Question

Find the volume, in cubic inches, of a cone with a radius of 11 inches and a height of 24 inches. Round your answer to the nearest hundredth.

Answer 1

To find the volume of a cone, we use the formula:

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

where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cone.

Given:
- Radius \( r = 11 \) inches
- Height \( h = 24 \) inches

We can plug these values into the formula:

\[
V = \frac{1}{3} \pi (11)^2 (24)
\]

Calculating \( (11)^2 \):

\[
11^2 = 121
\]

Now substituting back into the volume formula:

\[
V = \frac{1}{3} \pi (121)(24)
\]

Calculating \( 121 \times 24 \):

\[
121 \times 24 = 2904
\]

Now substituting this back into the equation for volume:

\[
V = \frac{1}{3} \pi (2904)
\]

Calculating \( \frac{2904}{3} \):

\[
\frac{2904}{3} = 968
\]

Now we substitute this into the formula for volume:

\[
V = 968 \pi
\]

Using the approximation \( \pi \approx 3.14159 \):

\[
V \approx 968 \times 3.14159 \approx 3042.11072
\]

Rounding to the nearest hundredth, we get:

\[
V \approx 3042.11
\]

Thus, the volume of the cone is

\[
\boxed{3042.11} \text{ cubic inches.}
\]