To find the volume of a cylindrical rain barrel, you can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where:
- \(V\) is the volume,
- \(r\) is the radius of the base,
- \(h\) is the height of the cylinder.
Given:
- The height (\(h\)) is 37 inches,
- The diameter is 22 inches, so the radius (\(r\)) is half of the diameter:
\[ r = \frac{diameter}{2} = \frac{22}{2} = 11 \text{ inches} \]
Now we can plug the values into the volume formula:
\[ V = \pi (11)^2 (37) \] \[ V = \pi (121) (37) \] \[ V = \pi (4477) \] \[ V \approx 3.14 \times 4477 \approx 14,052.58 \text{ cubic inches} \]
Choosing from the provided options, the closest to this calculation is:
14,057.78 inches³
Therefore, the volume of Hondo's rain barrel is approximately 14,057.78 cubic inches.