Question

If a square is inscribed in a circle, find the ratio of areas of the circle and the square. 

Answer 1

Let side of square be x cm which is inscribed in a circle.

Given,

Radius of circle (r) = \(\frac{1}{2}\) (diagonal of square)

= \(\frac{1}{2}\)(x√2)

r = x/√2

We know that, area of the square = x²

And, the area of the circle = πr²

Therefore, the ratio of areas of the circle and the square = π : 2