Question 1018930
a) If the square is inside the circle, the diameter({{{D[c]}}}) of the circle is equal to the diagonal of the square, {{{D[s]}}}.
{{{A[s]=s^2}}}
So then,
{{{D[s]^2=s^2+s^2=2s^2}}}
and
{{{A[c]=(pi/4)*D[c]^2}}}
{{{A[c]=(pi/4)*(2s^2)}}}
{{{A[c]=(pi/2)s^2}}}
So then,
{{{A[s]/A[c]=(s^2)/((pi/2)*s^2)}}}
{{{A[s]/A[c]=2/pi}}}
b) If the circle is inside the square then the diameter of the circle will equal a side of the square.
{{{A[s]=s^2}}}
{{{A[c]=(pi/4)D[c]^2=(pi/4)s^2}}}
So then,
{{{A[c]/A[s]=((pi/4)s^2)/s^2}}}
{{{A[c]/A[s]=pi/4}}}