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

1. **Find the radius from the diameter**:
The diameter of the cylinder is given as 40 feet, so the radius \( r \) is half of that:

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

2. **Substitute the values into the volume formula**:
We are given that the volume \( V \) is 31,400 cubic feet and \( \pi \) is approximated as 3.14. Now, substitute these values into the volume formula:

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

First, calculate \( 20^2 \):

\[
20^2 = 400
\]

Now, substitute this back into the equation:

\[
31,400 = 3.14 (400) h
\]

Simplifying further:

\[
31,400 = 1256 h
\]

3. **Solve for \( h \)**:
To find \( h \), divide both sides by 1256:

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

Now, performing the division:

\[
h \approx 25
\]

Thus, the height of the grain bin is approximately

\[
h \approx 25 \text{ feet}.
\]

So the final answer is:

\[
h = 25 \text{ ft}.
\]