Let us consider a rectangle inscribed in a circle with length a cm and breadth b cm ,

=== a^2 + b^2 = 400 ;; since 2*radius will be the daigonal of the rectangle

so we have to maximize Area of rectangle = a*b , subsituting the value of b in terms of a

we get Area^2 = (a^2)*(400 - a^2)

differentaiting and equating to zero we get a^2= 200 and b^2=200

so Area = a*b= 200

hence the remaining area will be = 3.14*100 - 200 = 114 cm^2