Set $18\pi$ equal to the circumference formula and solve the resulting equation for $r$. What do you get for the radius?

Once you know $r$, use the area formula for a circle, $A = \pi r^2$. Be careful not to forget the square on $r$.

In Desmos, type 18pi/(2pi) to compute $r = \frac{C}{2\pi}$. The output is the radius of the circle.

In a new line, type pi*(18pi/(2pi))^2 or, using the radius you just found, pi*(r)^2. This value is the area of the circle.

Type each answer choice into Desmos: 9pi, 81pi, 162, and 324pi. Compare their numerical values with the area you found in step 2 and select the choice that matches.

The circumference $C$ of a circle is related to its radius $r$ by

You are given $C = 18\pi$, so set up the equation

To find $r$, divide both sides of the equation by $2\pi$:

The $\pi$ cancels, and $18 \div 2 = 9$, so the radius is

The area $A$ of a circle with radius $r$ is

Substitute $r = 9$:

So the area of the circle is $81\pi$ square centimeters, which matches choice B.