Question

A cylindrical shaped silo has a diameter of 18 feet and a height of 4 feet. How much water can the silo hold, in terms of π?
Responses
A 162π
162π ft 3
B 324π
324π ft 3
C 648π
648π ft 3
D 1296π

Answer 1

To find the volume of a cylindrical silo, 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, and
- \(h\) is the height of the cylinder.

Given the diameter of the silo is 18 feet, we can calculate the radius:

\[
r = \frac{diameter}{2} = \frac{18}{2} = 9 \text{ feet}
\]

The height \(h\) of the silo is given as 4 feet.

Now we can substitute the values into the volume formula:

\[
V = \pi (9)^2 (4)
\]

Calculating \(9^2\):

\[
9^2 = 81
\]

Now substituting back into the volume formula:

\[
V = \pi \times 81 \times 4 = \pi \times 324
\]

Thus, the volume of the silo is:

\[
V = 324\pi \text{ ft}^3
\]

Therefore, the correct response is:

**B. 324π ft³**