Question

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

Answer 1

First let ABCD be the square inscribed in the circle.

Let diameter of circle be 2r.

Since square ABCD is inscribed in the circle , diagonal AC and BD will be equal to the diameter (2r)

therefore, BD = 2r

In triangle BCD inside square ABCD ,

BC2 + CD2 = BD2

BC2 + BC2 = (2r)2 ( BD = 2r , BC = CD)

2BC2 = 4r2

BC2 = 2r2

Ratio of Areas of circle and the square = area of circle / area of square = pie r2 / BC2 = 22 / 7 * r2 / 2r2 (BC2=2r2)

= 22 / 7 / 2

= 11 / 7