Find a function that models the radius r of a circle in terms of its area a

To model the radius r of a circle in terms of its area a, we start with the formula for the area of a circle, which is given by:

A = πr²

Where A is the area and r is the radius. To express r in terms of A, we need to manipulate this formula. Here are the steps:

1. Start with the area formula: A = πr²
2. To isolate r², divide both sides by π: r² = A / π
3. Now, take the square root of both sides to solve for r: r = √(A / π)

This gives us the radius r in terms of the area A. Therefore, the function that models the radius of the circle based on its area is:

r(A) = √(A / π)

This function allows you to calculate the radius of a circle if you know its area.