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, we can use the formula:

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

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

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

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

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

3. Now we can plug these values into the formula:

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

Calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

So now we have:

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

Calculating \( 36 \cdot 15 \):

\[
36 \cdot 15 = 540
\]

Now substituting back into the volume formula:

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

Calculating \( 3.14 \cdot 540 \):

\[
3.14 \cdot 540 = 1695.6
\]

Now divide by 3:

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

Therefore, the volume of the water tank is:

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