The circumference of a circle is given by the formula $C = 2\pi r$, where $r$ is the radius of the circle.
We are given that the circumference is 18 cm, so we can set up the equation $18 = 2\pi r$.
Solving for $r$, we find that $r = \frac{9}{\pi}$.
The area of a circle is given by the formula $A = \pi r^2$, so the area of this circle is $\pi \left(\frac{9}{\pi}\right)^2 = \boxed{\frac{81}{\pi}}$.
The answer is: \frac{81}{\pi}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
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 $\pi$.

### Answer:
