The circumference of a particular circle is 18 cm. In square centimeters, what is the area of the circle? Express your answer as a common fraction in terms of $\pi$.
If $r$ is the radius of the circle, then the circumference is $2\pi r$.  Setting $2\pi r$ equal to 18 cm, we find $r=9/\pi$ cm.  The area of the circle is $\pi r^2=\pi\left(\dfrac{9}{\pi}\right)^2=\boxed{\dfrac{81}{\pi}}$ square centimeters.