Question

A cylindrical water tank has a diameter of 20 feet and a height of 15 feet. How much water is needed to fill the tank?

Recall the formula V = pi r squared h.
300Pi cubic feet
1,500Pi cubic feet
2,250Pi cubic feet
6,000Pi cubic feet

Answer 1

To find the volume of a cylindrical water tank, we can use the formula:

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

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

Given:
- Diameter of the tank = 20 feet, so the radius \( r \) is half of that:

\[
r = \frac{20}{2} = 10 \text{ feet}
\]

- Height \( h = 15 \) feet.

Now, substituting the values into the formula:

\[
V = \pi (10)^2 (15)
\]

Calculating \( (10)^2 \):

\[
(10)^2 = 100
\]

Now, substituting back:

\[
V = \pi \times 100 \times 15
\]

Calculating \( 100 \times 15 \):

\[
100 \times 15 = 1500
\]

So, the volume is:

\[
V = 1500\pi \text{ cubic feet}
\]

Thus, the amount of water needed to fill the tank is

\[
\boxed{1500\pi} \text{ cubic feet}.
\]