To find the volume of a cylindrical rain barrel, 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, and
- \( h \) is the height.
- Calculate the radius: The diameter of the barrel is 22 inches, so the radius \( r \) is half of the diameter:
\[ r = \frac{diameter}{2} = \frac{22}{2} = 11 \text{ inches} \]
-
Height: The height \( h \) is given as 37 inches.
-
Calculate the volume:
Now we can substitute the values into the volume formula:
\[ V = \pi (11)^2 (37) \]
Calculating \( (11)^2 \):
\[ (11)^2 = 121 \]
Now plug this into the volume formula:
\[ V = \pi \times 121 \times 37 \]
Calculating \( 121 \times 37 \):
\[ 121 \times 37 = 4477 \]
Now, substitute this back into the formula for volume:
\[ V = \pi \times 4477 \]
Now using \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 4477 \approx 14057.78 \]
Therefore, the volume of the rain barrel is approximately:
\[ V \approx 14,057.78 \text{ inches}^3 \]
The correct response is:
14,057.78 inches^3