A circle is inscribed in a square. Write and simplify an expression for the ratio of the area of the square to the area of the circle. For a circle inscribed in a square, the diameter of the circle is equal to the side length of the square.

Best Answer: So first we need both areas, then we can relate them, and then divide the circle by the square:

A (circle) = πr^2

A (square) = L*W or (2r) * (2r) which is (2r) ^2

For the square, we know this is true because because the radius is half the diameter, so if we multiply the radius by 2, we get the length of one side of the square. We also know that the lengths of both sides of the square are the same by definition of a square.

Ratio: (πr^2) / (4r^2) = π/4