To solve for $r$ in the equation $A = \pi r^2$, follow these steps:

1. Start with the equation: $A = \pi r^2$

2. Divide both sides by $\pi$ to isolate $r^2$: $\frac{A}{\pi} = r^2$

3. Take the square root of both sides to solve for $r$: $r = \sqrt{\frac{A}{\pi}}$

Thus, the solution for $r$ is: $r = \sqrt{\frac{A}{\pi}}$

Would you like more details on this solution?

Here are some related questions:

1. What is the value of $r$ if $A = 50$ square units?
2. How does the equation change if the shape is an ellipse instead of a circle?
3. Can you express $r$ in terms of another variable related to circumference $C$?
4. What happens to $r$ if you double the area $A$?
5. How is this formula derived from the basic geometry of a circle?

Tip: Always double-check the units of $A$ to ensure correct application of the formula.