The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cone is 216π units and the height is 18 units. Substituting these values into the formula, we get:
216π = (1/3)πr^2(18)
Simplifying this equation, we get:
r^2 = (216π x 3) / (18π)
r^2 = 36
r = 6
Therefore, the radius of the cone is 6 units.