To find the volume of the cone, we can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
Given:
- Radius \( r = 12 \) cm
- Height \( h = 18 \) cm
Now, substituting these values into the formula:
\[ V = \frac{1}{3} \pi (12)^2 (18) \]
Calculating \( (12)^2 \):
\[ (12)^2 = 144 \]
Now substituting this back into the formula:
\[ V = \frac{1}{3} \pi (144)(18) \]
Calculating \( 144 \times 18 \):
\[ 144 \times 18 = 2592 \]
Now substitute that back in:
\[ V = \frac{1}{3} \pi (2592) \]
Calculating \( \frac{2592}{3} \):
\[ \frac{2592}{3} = 864 \]
Thus, the volume of the cone is:
\[ V = 864 \pi , \text{cm}^3 \]
So the volume of the cone is \( \boxed{864 \pi , \text{cm}^3} \).
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