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
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Answer 1

To find the height of the 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, and \( h \) is the height.

Given:
- Volume \( V = 31,400 \) cubic feet
- Diameter = 40 feet, so the radius \( r = \frac{40}{2} = 20 \) feet
- Using \( \pi \approx 3.14 \)

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

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

First, calculate \( 20^2 \):

\[
20^2 = 400
\]

Now substitute that value back into the equation:

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

Calculate \( 3.14 \times 400 \):

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

Now the equation is:

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

Next, solve for \( h \):

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

Now, perform the division:

\[
h \approx 25
\]

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