Question

A cylindrical grain bin on a farm has a volume of 31,400 cubic feet. Find the height of the grain bin if the cylinder’s diameter is 40 feet long. Use 3.14 for π .(1 point)
h=
ft.

Answer 1

To find the height \( h \) of the cylindrical grain bin, we can use the formula for the volume \( V \) of a cylinder:

\[
V = \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.

Given:
- The volume \( V = 31,400 \) cubic feet,
- The diameter \( d = 40 \) feet.

First, we need to find the radius \( r \):

\[
r = \frac{d}{2} = \frac{40 \text{ ft}}{2} = 20 \text{ ft}
\]

Now, we can plug the values into the volume formula and solve for \( h \):

\[
31,400 = 3.14 \times (20)^2 \times h
\]

Calculating \( (20)^2 \):

\[
(20)^2 = 400
\]

Now substitute this value into the volume formula:

\[
31,400 = 3.14 \times 400 \times h
\]

Calculating \( 3.14 \times 400 \):

\[
3.14 \times 400 = 1256
\]

Now we have:

\[
31,400 = 1256 \times h
\]

To find \( h \), divide both sides by 1256:

\[
h = \frac{31,400}{1256}
\]

Calculating \( h \):

\[
h \approx 25
\]

Thus, the height \( h \) of the grain bin is approximately \( 25 \) feet.

\[
\boxed{25} \text{ ft}
\]