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)
cubic feet

Answer 1

To find the volume of a cone, you can use the formula:

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

where \( V \) is the volume, \( r \) is the radius of the base of the cone, and \( h \) is the height of the cone.

1. First, find the radius of the cone. The diameter is given as 12 feet, so the radius \( r \) is:

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

2. The height \( h \) of the cone is given as 15 feet.

3. Now, substitute the values into the volume formula:

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

4. Calculate \( (6)^2 \):

\[
(6)^2 = 36
\]

5. Now substitute this back into the volume equation:

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

6. Calculate \( 36 \times 15 \):

\[
36 \times 15 = 540
\]

7. Now substitute that back into the equation:

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

8. Calculate \( 3.14 \times 540 \):

\[
3.14 \times 540 = 1695.6
\]

9. Finally, calculate the volume:

\[
V = \frac{1}{3} \times 1695.6 \approx 565.2
\]

So the volume of the tank is approximately:

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