To find the volume of the rain barrel, which is a cylindrical shape, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
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First, we need to find the radius of the cylinder. The diameter given is 22 inches, so the radius \( r \) is: \[ r = \frac{\text{diameter}}{2} = \frac{22}{2} = 11 \text{ inches} \]
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The height \( h \) of the barrel is given as 37 inches.
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Now we can substitute the radius and height into the volume formula: \[ V = \pi (11^2) (37) \] \[ V = \pi (121) (37) \] \[ V = \pi (4477) \]
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The volume is then approximately: \[ V \approx 3.14159 \times 4477 \approx 14066.7 \text{ inches}^3 \]
Considering the available response choices, the closest volume is:
14,057.78 inches³
So, the correct answer is:
14,057.78 inches cubed.