Let ABCD be a square inscribed in a circle of radius 'r'. Now, the diameter of circle is the diagonal of square.Therefore, BD=2r. In △BDC, using Pythagoras theorem BC2+CD2=BD2⇒a2+a2=(2r)2⇒2a2=4r2⇒a2=2r2∴Area of square=2r2Area of circle=πr2Required ration=πr2:2r2=π:2