The area of a circle is given by the formula:

$A = \pi r^2$

For a circle with a radius of 3 cm, we substitute $r = 3$ into the formula. Thus, the area is:

$f(3) = \pi (3)^2 = 9\pi \, \text{square cm}$

So, the area of a circle with a radius of 3 cm is $9\pi \, \text{square cm}$.

Would you like more details or clarification?

Here are some related questions:

1. How do you find the area of a circle using the radius in function notation?
2. How does the area of a circle change if the radius is doubled?
3. How would you calculate the radius if you know the area of the circle?
4. What is the significance of the constant $\pi$ in the formula for the area of a circle?
5. How can you express the area of a circle in terms of diameter instead of radius?

Tip: Remember, the area formula $A = \pi r^2$ is based on the radius squared, so even small changes in the radius can lead to significant changes in the area!