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.
18\pi
Level 2
Geometry
Problem: 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]
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the volume of the cone, we need to use the formula for the volume of a cone, which is given by \( V = \frac{1}{3} \pi r^2 h \). 

We know the volume of the cylinder is \( 54\pi \) cm³. The formula for the volume of a cylinder is \( V = \pi r^2 h \). 

Setting the volume of the cylinder equal to \( 54\pi \), we have:
\[
\pi r^2 h = 54\pi
\]
Dividing both sides by \( \pi \) gives:
\[
r^2 h = 54
\]

Since the cone has the same radius \( r \) and height \( h \) as the cylinder, we can substitute \( r^2 h \) into the cone's volume formula:
\[
V_{cone} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (r^2 h)
\]
Substituting \( r^2 h = 54 \) into the equation results in:
\[
V_{cone} = \frac{1}{3} \pi (54) = \frac{54\pi}{3}
\]
Calculating \( \frac{54}{3} \) yields \( 18 \). 

Thus, the volume of the cone is:
\[
V_{cone} = 18\pi
\] 

The final answer is \( 18\pi \).<|END_OF_LATENT|> The final answer is $18\pi$.