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.
- First, we need to find the radius \( r \). The diameter of the tank is given as 12 feet, so the radius is:
\[ r = \frac{diameter}{2} = \frac{12}{2} = 6 \text{ feet} \]
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The height \( h \) is given as 15 feet.
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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:
\[ \boxed{565.2} \text{ cubic feet} \]
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