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 pi

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 of the cylinder,
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a mathematical constant (approximately 3.14 in this case).

Given the volume \( V = 31,400 \) cubic feet and the diameter of the cylinder is 40 feet, we can first find the radius \( r \):

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

Now we can substitute 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 back into the equation:

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

Calculating \( 3.14 \times 400 \):

\[
3.14 \times 400 = 1256
\]

Now we have:

\[
31,400 = 1256h
\]

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

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

Now, perform the division:

\[
h \approx 25
\]

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