Question

Hondo wants to buy a rain barrel. Solve for the volume of the barrel if the height is 37 inches and the diameter is 22 inches.(1 point)
Responses

2,555.96 inches3
2
,
555.96

inches
3
2,555.96 inches cubed

56,231.12 inches3
56
,
231.12

inches
3
56,231.12 inches cubed

1,277.98 inches3
1
,
277.98

inches
3
1,277.98 inches cubed

14,057.78 inches3

Answer 1

To find the volume of the rain barrel, which is in the shape of a cylinder, 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.

1. **Determine the radius**: The diameter is given as 22 inches, so the radius \( r \) is half of that:

\[
r = \frac{diameter}{2} = \frac{22}{2} = 11 \text{ inches}
\]

2. **Height**: The height \( h \) is given as 37 inches.

3. **Calculate the volume**:
- Plug in the values into the volume formula:

\[
V = \pi (11)^2 (37)
\]

Calculating \( (11)^2 \):

\[
(11)^2 = 121
\]

Now substitute back into the volume formula:

\[
V = \pi \times 121 \times 37
\]

Calculating \( 121 \times 37 \):

\[
121 \times 37 = 4477
\]

Now substitute this value back:

\[
V = \pi \times 4477
\]

Using an approximate value for \( \pi \) (3.14159):

\[
V \approx 3.14159 \times 4477 \approx 14059.77
\]

Thus, rounding this value gives us approximately:

\[
V \approx 14,057.78 \text{ cubic inches}
\]

So the volume of the rain barrel is approximately **14,057.78 inches³**.

The correct response is:
**14,057.78 inches³**.