Question

A farmer wants to know how much corn he is going to sell at the end of the season. He stores the corn in a silo, which is in the shape of a right circular cylinder. If the height is 40 feet, and the diameter is 15 feet, what is the volume? Use 3.14
for π
.

Answer 1

To find the volume of a right circular cylinder, you can use the formula:

\[
V = \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.

First, we need to find the radius \( r \). The diameter of the cylinder is 15 feet, so the radius is:

\[
r = \frac{\text{diameter}}{2} = \frac{15}{2} = 7.5 \text{ feet}
\]

Now, let's use the values we have to calculate the volume:

- \( r = 7.5 \) feet
- \( h = 40 \) feet
- \( \pi \approx 3.14 \)

Substituting these values into the volume formula:

\[
V = 3.14 \times (7.5)^2 \times 40
\]

Calculating \( (7.5)^2 \):

\[
(7.5)^2 = 56.25
\]

Now, substitute this back into the volume formula:

\[
V = 3.14 \times 56.25 \times 40
\]

Calculating \( 3.14 \times 56.25 \):

\[
3.14 \times 56.25 \approx 176.625
\]

Finally, multiply by 40:

\[
V \approx 176.625 \times 40 \approx 7065
\]

Thus, the volume of the silo (the amount of corn the farmer will sell) is approximately:

\[
\boxed{7065} \text{ cubic feet}
\]