SOLUTION: Dear Sir I want calculate length of the plastic film winded on 76.5mm- ID (Inner Diameter)and 104.5mm- OD (Outer diameter)of cylinder? Thickness of plastic film is 20micron

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Question 12230: Dear Sir
I want calculate length of the plastic film winded on 76.5mm- ID (Inner Diameter)and 104.5mm- OD (Outer diameter)of cylinder?
Thickness of plastic film is 20micron
Diameter of the roll after winding film is 600mm

If you have formula to calculate then can you please tell me.
Thank you
Best Regards

Answer by kusha(21) (Show Source):
You can put this solution on YOUR website!
ID = 76.5 thus Inner Radius = 38.25mm
OD = 104.5 thus Outer Radius = 52.25 mm
Thus thickness of roll on a side is 52.25 - 38.25 = 14 mm
Thickness of film is 20 Micron and 1 micron = 1/1000 mm
therefore thickness is 1/50 mm or 0.02 mm
Dividing total thickness by thickness of one strip we get 14/(1/50) = 700 rolls
The radius of 1st layer is (IR + thickness of film)38.25 + 0.02 mm
The radius of next layer is 38.25 + 0.04 mm
The radius of third layer is 38.25 + 0.06 mm AND SO ON FOR 70 layers.
this becomes an Arithematic Progression with first term 38.27mm and common difference ( d) as 0.02 mm
We have to calculate circumferences of all these layers and add them. The Circumference formula is 2x(22/7)x R
Therefore sum of circumferences is
2x(22/7)x 38.25 + 2x(22/7)x 38.27 + upto 70 terms
=2x(22/7)x{38.25+38.27 +-----upto 70 terms)
= 44/7 x (70/2)(2x38.25 + (69x0.02) sum of n terms of AP (n/2){2a+(n-1)d}
= 1557.6 mm after solving above expression