Question

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

Answer 1

When a square inscribed in a circle 

then, 

Diameter of circle = diagonal of square 

Let side of the square be = a cm 

Diagonal of square be = \(\sqrt{2a}\) cm

Area of square = a² cm² 

Diameter of circle = \(\sqrt{2a}\) cm

؞ radius of circle = \(\frac{\sqrt2a}{2}\) = \(\frac{a}{\sqrt2}\)

Area of circle = π x \(\frac{a^2}{2}\) cm

Ratio of area of circle and square = \(\frac{πa^2}2\) : a²

= π : 2