Assume a circle of radius r has the same area as a square with side length s. express the radius of the circle in terms of the length of a side of the square (i. e. write r as a function of s)

r = √s^2/ π

Step-by-step explanation:

Let r represent radius of the circle.

Let s represent the side of the square.

The formula for the area of a circle is expressed as

Area of circle = πr^2

Where π is a constant. So

Area of the circle = πr^2

The formula for the area of a square is expressed as

Area of square s × s = s^2

Where s = length of one side of the square.

We want to express the radius of the circle in terms of the length of the side of the square

Assuming the circle has the same area as a square, it means that

πr^2 = s^2

r^2 = s^2/ π

r = √s^2/ π