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.

h = __ ft.

Answer 1

To find the height of a cylindrical grain bin given the volume and diameter, you 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 base, and
- \( h \) is the height.

1. **Calculate the radius**:
The diameter of the cylinder is 40 feet, so the radius \( r \) is half of the diameter:

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

2. **Use the volume to find the height**:
Given the volume \( V = 31,400 \) cubic feet, plug in the values into the volume formula.

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

Calculate \( (20)^2 \):

\[
(20)^2 = 400
\]

Substitute this back into the equation:

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

Calculate \( 3.14 \times 400 \):

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

So the equation becomes:

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

3. **Solve for \( h \)**:

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

Now perform the division:

\[
h = 25
\]

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