A person has a rectangular sheet of metal.He has to make cylindrical vessel whose both circular ends are closed.When he minimizes the wastage of the sheet,then what is the ratio of the wasted sheet to the utilised sheet?

(1) . 1/22

(2) . 3/11

(3) . 1/11

(4) . 5/22

Asked by dfojajjar | 17th Feb, 2020, 01:07: PM

Expert Answer:

As shown in figure, if cylinder with closed ends are made by a rectangular sheet and wastage is minimised,
then dimensions of rectangular sheet should be (π+1)d × 2d
 
area of sheet to make cylinder = πd × 2d +(1/2)πd2 = (5/2)πd2
 
wasted area = 2(π+1)d2 - (5/2)πd2 = [ 2 -(π/2)]d2
 
ratio of wasted area to utilised area = [ 2 -(π/2)] / [ (5/2)π ] ≈ 0.055

Answered by Thiyagarajan K | 17th Feb, 2020, 04:05: PM