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. Regards 

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

