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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?

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?

Grade:11

3 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
5 years ago
zThe length of the square sheet will be equal to 4r + h .
From this information you can relate both the values in a common variable and you will get the ratio.
Ayush
23 Points
5 years ago
why the length will be 4r+h.............................................................................................................?
 
Akhil
13 Points
2 years ago
Let length l
 Breadth b hence radius
r=b/4
h=b=4r
2πr=l-2r
58r/7=l
lb=232r²/7
2πrh+2πr²=176r²/7 + 44+r²/7=220r²/7
Difference=12r²/7
Ratio=12/220=3/55

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