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 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 of the cylinder,
- \( h \) is the height of the cylinder.

1. First, we need to find the radius. The diameter of the cylinder is given as 40 feet, so the radius \( r \) is:

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

2. Now, we can plug the values into the volume formula. We know \( V = 31,400 \) cubic feet, \( \pi \approx 3.14 \), and \( r = 20 \) feet:

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

3. Calculate \( (20)^2 \):

\[
(20)^2 = 400
\]

4. Substitute this back into the equation:

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

5. Now calculate \( 3.14 \times 400 \):

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

6. The equation now is:

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

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

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

8. Calculating this gives:

\[
h \approx 25
\]

Therefore, the height of the cylindrical grain bin is approximately \( \boxed{25} \) feet.