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.
Answers
GPT-4o mini
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,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14.
Given that the diameter of the cylinder is 40 feet, we can find the radius:
\[
r = \frac{\text{diameter}}{2} = \frac{40}{2} = 20 \text{ feet}
\]
Now, substituting the known values into the volume formula:
\[
31,400 = 3.14 \times (20)^2 \times h
\]
Calculate \( (20)^2 \):
\[
(20)^2 = 400
\]
Substituting that back into the equation:
\[
31,400 = 3.14 \times 400 \times h
\]
Calculating \( 3.14 \times 400 \):
\[
3.14 \times 400 = 1,256
\]
Thus, the equation now is:
\[
31,400 = 1,256h
\]
To solve for \( h \), divide both sides by 1,256:
\[
h = \frac{31,400}{1,256}
\]
Calculating that:
\[
h \approx 25
\]
Therefore, the height of the grain bin is approximately:
\[
\boxed{25} \text{ feet}
\]
\[
V = \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14.
Given that the diameter of the cylinder is 40 feet, we can find the radius:
\[
r = \frac{\text{diameter}}{2} = \frac{40}{2} = 20 \text{ feet}
\]
Now, substituting the known values into the volume formula:
\[
31,400 = 3.14 \times (20)^2 \times h
\]
Calculate \( (20)^2 \):
\[
(20)^2 = 400
\]
Substituting that back into the equation:
\[
31,400 = 3.14 \times 400 \times h
\]
Calculating \( 3.14 \times 400 \):
\[
3.14 \times 400 = 1,256
\]
Thus, the equation now is:
\[
31,400 = 1,256h
\]
To solve for \( h \), divide both sides by 1,256:
\[
h = \frac{31,400}{1,256}
\]
Calculating that:
\[
h \approx 25
\]
Therefore, the height of the grain bin is approximately:
\[
\boxed{25} \text{ feet}
\]