The length of paper on a tightly wound roll needs to be determined. The roll of paper has inner radius V and outer radius W. The thickness of the paper is 1 mm (0.001 m).

Using calculus, calculate the length of paper on the roll. After doing this for general V and W, evaluate the results for V = 3 cm, W = 13 cm.

Hint: find a function in polar coordinates which traces the coiled paper and calculate the arc length of that curve.