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