To find the volume of a cone, we can use the following 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, and
- \( \pi \) is a constant (approximately 3.14).
First, we need to determine the radius \( r \) of the base of the cone. The diameter is given as 12 feet, so the radius is:
\[ r = \frac{diameter}{2} = \frac{12}{2} = 6 \text{ feet} \]
The height \( h \) of the cone is given as 15 feet.
Now we can substitute 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 substitute this value in:
\[ V = \frac{1}{3} \times 3.14 \times 36 \times 15 \]
Calculating \( 36 \times 15 \):
\[ 36 \times 15 = 540 \]
Now substitute this back in:
\[ V = \frac{1}{3} \times 3.14 \times 540 \]
Calculating \( 3.14 \times 540 \):
\[ 3.14 \times 540 = 1695.6 \]
Now, we divide by 3:
\[ V = \frac{1695.6}{3} = 565.2 \]
Therefore, the volume of the water tank is approximately:
\[ \boxed{565.2} \text{ cubic feet} \]
Rounded to the nearest tenth, the answer is 565.2 cubic feet.