We are given the equation for the area of a circle:

$A = \pi r^2$

We need to solve for $r$ in terms of $A$.

Steps to Solve:

1. Isolate $r^2$: Divide both sides of the equation by $\pi$ to remove the constant:

   $\frac{A}{\pi} = r^2$

2. Solve for $r$: Take the square root of both sides. Remember that the square root introduces both positive and negative roots, but in this context, $r$ (radius) is non-negative:

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

Final Answer:

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

Would you like me to explain the steps in more detail or provide an example?

Related Questions:

1. If $A = 25\pi$, what is the value of $r$?
2. Solve for $r$ if $A = 78.5$ and $\pi \approx 3.14$.
3. Derive the formula for $A$ in terms of $r$ if the equation is reversed.
4. How would the formula change if we used circumference instead of area?
5. What is the geometric meaning of $r$ in this equation?

Tip:

To isolate a variable in a formula, use inverse operations step by step, such as addition, subtraction, multiplication, division, and roots.