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

Given:

$A = \pi r^2$

Solve for $r$:

1. Divide both sides of the equation by $\pi$: $\frac{A}{\pi} = r^2$

2. Take the square root of both sides: $r = \sqrt{\frac{A}{\pi}}$

Final Solution:

$r = \sqrt{\frac{A}{\pi}}$

Here, $A$ is the area of the circle, and $r$ is the radius.

Would you like an example with specific values for $A$ or a step-by-step breakdown?

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Questions for Expansion:

1. How is the formula $A = \pi r^2$ derived geometrically?
2. Can we calculate $r$ for specific values of $A$?
3. What are some applications of this formula in real life?
4. What happens to $r$ if $A$ is doubled or halved?
5. Can this formula be extended to other shapes, like ellipses?

Tip:

Always check your units when calculating radius; if $A$ is in square meters, $r$ will be in meters.