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

Answer 1

To find the height 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.

Given:
- The volume \( V = 31,400 \) cubic feet,
- The diameter of the cylinder \( d = 40 \) feet, which means the radius \( r = \frac{d}{2} = \frac{40}{2} = 20 \) feet.

Now we can substitute π and the values into the volume formula:

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

Calculating \( 20^2 \):

\[
20^2 = 400
\]

Now substitute back into the equation:

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

Calculating \( 3.14 \times 400 \):

\[
3.14 \times 400 = 1256
\]

Now the equation is:

\[
31,400 = 1256h
\]

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

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

Calculating the height \( h \):

\[
h \approx 25
\]

Thus, the height of the grain bin is approximately **25 feet**.