From a circular disc of radius 10 cm, a rectangle of maximum area is cut. What would be the area of the remaining disc?

Question

Answer 1

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

Answer 2

area of the circle is 100*pi sq cm or 314.159 sq cm
the largest rectangle will be a square
the side of the square is two times 0.7071 times the radius or 14.142 cm
thus area of the square is 200 sq cm
hence area around the square is 114.159 sq cm