So in this problem I am supposed to calculate the total length of a fabric wrapped around a cylinder.

I am given the following:

Thickness of the fabric: t

Cylinder diameter: c

Total diameter of all of the fabric and the cylinder together: d

I originally solved this problem by summing the circumference of each layer of fabric, using an incremental increase in diameter with the value of the thickness. However, I am looking for a way to solve this without the use of a sum.

I'm kind of lost as to where to start this though. I am assuming that the rate of change of thickness is a continuous function (as opposed to a step at the beginning of each layer). Any help in solving this problem would be greatly appreciated.