The volume of a cylinder is $54\pi$ $\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder? Express your answer in terms of $\pi$. [asy]
import solids; currentprojection=orthographic(0,100,25); defaultpen(linewidth(0.8));
revolution cyl = cylinder((5,0,0),1,5,Z);
revolution cone = cone((0,0,0),1,5,Z);
draw(cyl,backpen=dashed);
draw(cone,backpen=dashed);

[/asy]
A cone with radius $r$ and height $h$ has volume $(1/3)\pi r^2 h$; a cylinder with the same radius and height has volume $\pi r^2 h$.  Thus we see the volume of the corresponding cone has 1/3 the volume of the cylinder, which is $(1/3)(54\pi = \boxed{18\pi}$ cubic cm.