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,
- \(h\) is the height.
Given:
- The diameter of the cone is 12 feet, so the radius \(r\) is half of that:
\[ r = \frac{12}{2} = 6 \text{ feet} \]
- The height \(h\) is 15 feet.
Now, substituting the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (6^2) \times 15 \]
Calculating \(6^2\):
\[ 6^2 = 36 \]
Now substituting that back into the volume equation:
\[ V = \frac{1}{3} \times 3.14 \times 36 \times 15 \]
Calculating \(36 \times 15\):
\[ 36 \times 15 = 540 \]
Now substituting that value 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 taking one third of that:
\[ V = \frac{1695.6}{3} = 565.2 \]
Therefore, the volume of water that the tank can hold is
\[ \boxed{565.2} \text{ cubic feet.} \]