A square is inscribed in a circle (given)
Let r be the radius of circle and ‘x’ be the side of the square.
So, length of the diagonal = 2r
Length of side of square = x = diagonal/√2
= 2r/√2
= √2r
Area of square = (side)2 = ( x)2
= √2r × √2r
= 2r2
Area of circle = πr2
Ratio of areas of circle and square = (area of the circle)/(area of square)
= πr2 / 2r2
= π/2
Hence, the ratio of areas of circle and square is π:2.