A square is inscribed in a circle. Calculate the ratio of the area of the circle and the square.

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Solution

$L e t t h e r a d i u s o f t h e c i r c l e = r u n i t s N o w, a s p e r g i v e n d i a g o n a l o f s q u a r e = d i a m t e r e o f c i r c l e A n d w e k n o w t h a t t h e d i a g o n a l o f a s q u a r e o f a s i d e' a' u n i t s i s g i v e n b y \sqrt{2} a s o, \sqrt{2} a = 2 r a = \sqrt{2} r N o w, a r e a o f t h e c i r c l e = {πr}^{2} Area of square = a^{2} = {(\sqrt{2} r)}^{2} = 2 r^{2} therefore, required ratio = {πr}^{2} / 2 r^{2} = π : 2$

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