A rectangular sheet of length 42 cm and breadth 14 cm is cut from a circular sheet. What is the minimum area (in cm2) of circular sheet?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 1540
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 :-
AC2 = AB2 + BC2
⇒ (2r)2 = (42)2 + (14)2
⇒ 4r2 = (142)(32) + (142).
⇒ 4r2 = (142)(9 + 1) = 196 × 10.
⇒ r2 = 49 × 10 = 490 ………… (1)
Minimum area of circular sheet of paper = πr2
= (22/7) × 490 = 1540 cm2