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A blacksmith has a rectangular sheet of iron. He has to make a cylindrical vessel both circular ends are closed. When he minimizes the wastage of the sheet of iron, then what is the ratio of the wastage to the utilised area of sheet?
Asked by jagdishdabang79 | 18 Mar, 2024, 08:40: PM

Figure shows the fabrication of hollow cylinder with both sides closed from  a rectangula sheet with minimum wastage.

As shown in figure, width of rectangular sheet equals 2D where D is diameter of cylinder .

Circumference of cylinder is πD , hence length of rectangular sheet is ( π+1) D .

AS shown in figure , wasted area, WA =  2D2 - (π/4)D2 - (π/4)D2 = [ 2 - (π/2) ] D2

Utilised area , UA = 2 π D2 + (π/4)D2 + (π/4)D2

Ratio of wasted area to utilised area = [ 2 - (π/2) ] / [ 2 + (π/2) ] = 0.120

If we compare the list of options , the ratio 2/17 ≈ 0.120

Hence the answer :- Ratio of wasted area to utilised areais (2/17)

Answered by Thiyagarajan K | 19 Mar, 2024, 06:18: PM

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