Question 1205152


We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.

 {{{d = 2r}}}

we also know that the area of square is

{{{A=(1/2)d^2}}}

substituting {{{d=2r}}}, area is

{{{A=(1/2)(2r)^2}}}

{{{A=(1/2)4r^2}}}

{{{A=2r^2}}} => the area of square expressed in terms of radius


 the area of the circle

{{{A[c]=pi*r^2}}}


 the ratio of the area of the square to the area of the circle

{{{A/A[c]=(2r^2)/(pi*r^2)=2/pi}}}