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, and \( h \) is the height.

Given:
- Volume \( V = 31,400 \) cubic feet
- Diameter \( d = 40 \) feet

First, we need to calculate the radius:

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

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 back into the equation:

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

Now calculate \( 3.14 \times 400 \):

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

Now our equation looks like this:

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

Next, solve for \( h \):

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

Calculating the division:

\[
h \approx 25
\]

Thus, the height \( h \) of the grain bin is:

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

So, the answer is:

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