Question

A water tank in the shape of a cone has a diameter of 12 feet and a height of 15 feet. What volume of water, in cubic feet, can the tank hold? Round your answer to the nearest tenth and use 3.14 for π .(1 point)

(blank) cubic feet

Answer 1

To find the volume of a cone, we use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

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

Given:
- The diameter of the cone is 12 feet, so the radius \( r \) is:

\[
r = \frac{12}{2} = 6 \text{ feet}
\]

- The height \( h \) is 15 feet.

Now we substitute the values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (6^2) \times 15
\]

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Now substituting back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 36 \times 15
\]

Calculating \( 36 \times 15 \):

\[
36 \times 15 = 540
\]

Now substituting that back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 540
\]

Calculating \( 3.14 \times 540 \):

\[
3.14 \times 540 = 1695.6
\]

Now dividing by 3:

\[
V = \frac{1695.6}{3} = 565.2
\]

So the volume of the water tank is:

\[
\boxed{565.2} \text{ cubic feet}
\]