Let’s solve the problem step by step:

1. Given information:

   • Circumference of the circle is $6\pi$ cm.
   • Formula for the circumference of a circle is $C = 2\pi r$, where $r$ is the radius.

2. Find the radius $r$: $C = 2\pi r \implies 6\pi = 2\pi r$ Divide both sides by $2\pi$: $r = \frac{6\pi}{2\pi} = 3 \, \text{cm.}$

3. Formula for the area of a circle: $A = \pi r^2$

4. Substitute $r = 3$: $A = \pi (3)^2 = \pi \cdot 9 = 9\pi \, \text{cm}^2$

Final Answer:

$A = 9\pi \, \text{cm}^2$

Would you like further clarification or more detailed steps?

Here are 5 related questions for further practice:

1. If the radius of a circle is $4 \, \text{cm}$, what is its circumference in terms of $\pi$?
2. A circle has an area of $25\pi \, \text{cm}^2$. What is its radius?
3. How does doubling the radius affect the area of a circle?
4. If the diameter of a circle is $10 \, \text{cm}$, what is its area in terms of $\pi$?
5. What is the relationship between the radius and area of a circle?

Tip: Always identify key formulas for circles: $C = 2\pi r$ and $A = \pi r^2$.