Question

A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.

Answer 1

Let the side of the square be a and radius of the circle be r
We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.

`∴ sqrt(2a) = 2r`

`⇒ a = sqrt(2r)`

Now ,

`"Area of circle"/"Area of square" = (pi"r"^2)/"a"^2`

`= (pi"r"^2)/(sqrt(2r))^2`

`= ( pi"r"^2)/(2pi^2)`

`= pi/2`

Hence, the ratio of the areas of the circle and the square is π : 2