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.).