The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
For the cone with a radius of \( 12 \) cm and a height of \( 18 \) cm, we can substitute these values into the formula:
\[ V = \frac{1}{3} \pi (12)^2 (18) \]
First, calculate \( (12)^2 \):
\[ (12)^2 = 144 \]
Next, substitute \( 144 \) back into the volume formula:
\[ V = \frac{1}{3} \pi (144) (18) \]
Now, multiply \( 144 \) by \( 18 \):
\[ 144 \times 18 = 2592 \]
So the volume becomes:
\[ V = \frac{1}{3} \pi (2592) \]
Now divide \( 2592 \) by \( 3 \):
\[ \frac{2592}{3} = 864 \]
Thus, the volume of the cone is:
\[ V = 864 \pi \text{ cm}^3 \]
Therefore, the answer is:
864 pi cm^3