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.

A. 3,039.52 cu in
B. 828.96 cu in
C. 2,486.88 cu in
D. 9,118 cu in

Answer 1

The volume \( V \) of a cone can be calculated using the formula:

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

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

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

Now substituting the values into the formula:

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

Calculating \( 11^2 \):

\[
11^2 = 121
\]

Now substituting that back into the volume formula:

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

Calculating \( 121 \times 24 \):

\[
121 \times 24 = 2904
\]

Now our formula for volume becomes:

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

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

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

Now we multiply by \( \pi \):

\[
V = 968 \pi
\]

Using the approximate value of \( \pi \approx 3.14159 \):

\[
V \approx 968 \times 3.14159
\]

Calculating the volume:

\[
V \approx 3042.74192
\]

Now rounding to the nearest hundredth:

\[
V \approx 3042.74 \text{ cu in}
\]

Among the options provided, none of them match exactly. However, the closest option seems to be:

**A. 3,039.52 cu in**

So, the answer to the volume of the cone is approximately:

**3042.74 cubic inches** (closest choice **A.**).