A rectangular sheet of length 42 cm and breadth 14 cm is cut from a circular sheet. What is the minimum area (in cm$$^2$$) of circular sheet?

Let ABCD is a rectangular sheet of paper which has cut from a circular sheet of

paper. AB=CD=42 cms. and BC=AD=14 cms. Thus diagonal AC or. BD will be

the diameter of the circle. In right angled triangle ABC :-

$$AC^2= AB^2+BC^2$$

or, $$(2.r)^2= (42)^2+(14)^2$$

or, $$4.r^2= (14^2).(3^2) +(14^2).$$

or, $$4.r^2=(14^2).(9+1)= 196×10.$$

or, $$r^2 = 49×10 = 490…………(1)$$

Minimum area of circular sheet of paper$$= π.r^2. , putting r^2=490 from eqn. (1).$$

=(22/7)×490= 1540 sq.unit.

B is correct choice.