Quandaries and Queries


How would you calculate a diameter of a paper reel when the paper is 0,04 millimeters thick and for example 5000 meters of it is winded on a 76 mm (3inch) core.





Think of the paper laid out as one long piece. The edge of this paper strip is a very long, thin rectangle of some length L and thickness t.

This long, thin rectangle has area t L.

Now roll the paper onto the reel and look at the end of the roll. Let R be its radius and r the radius of the core.

The edge of the paper in now in the shape of a disk of radius R with a hole in its center of radius r. The area of this region is

R2 - r2 = (R2 - r2)

But the area of the edge of the paper has not changed, only its shape has changed. Hence

t L = (R2 - r2)



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