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 of a cylindrical grain bin, 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.

Given:
- The volume \( V = 31,400 \) cubic feet,
- The diameter of the cylinder is 40 feet, so the radius \( r \) is half of the diameter:

\[
r = \frac{diameter}{2} = \frac{40}{2} = 20 \text{ feet}
\]

Now we can substitute \( V \) and \( r \) 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 back into the volume equation:

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

Calculating \( 3.14 \times 400 \):

\[
3.14 \times 400 = 1,256
\]

Now we have:

\[
31,400 = 1,256 \times h
\]

To find \( h \), divide both sides by 1,256:

\[
h = \frac{31,400}{1,256}
\]

Calculating \( h \):

\[
h \approx 25
\]

Thus, the height of the grain bin is:

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