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, and \( \pi \) is approximately 3.14.
Given that the diameter of the cone is 12 feet, we can calculate the radius:
\[ r = \frac{diameter}{2} = \frac{12}{2} = 6 \text{ feet} \]
The height \( h \) is given as 15 feet. Now, we can plug in 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 this 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 substitute this back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 540 \]
Calculating \( 3.14 \times 540 \):
\[ 3.14 \times 540 = 1695.6 \]
Now divide by 3:
\[ V = \frac{1695.6}{3} \approx 565.2 \]
So the volume of water that the tank can hold is approximately
\[ \boxed{565.2} \text{ cubic feet} \]