Here's an easy problem. If 500 sheets of 20 lb. paper make a stack 2 inches high, we can easily get a value for the average thickness (0.004 inches) of a piece of paper. (Here thickness is the average distance from the top of one piece of paper to the top of the next piece of paper.)

Here's a harder problem. In a similar manner we wish to find the thickness of a sheet of toilet paper. In general, we have a roll of toilet paper with n sheets, each of length l, an inner radius r where the sheets start, and an outer radius R where the roll ends.

1) Find the average thickness, d, of a sheet of the toilet paper in terms of R, r, n, and l.
Note that we can get the thickness d of any roll of paper in terms of R, r, and L, where L is the total length of the roll if it were unrolled. (Obviously L = n×l.)

2) Find the average thickness of a sheet from a roll with stated values: n = 425 sheets, l = 4 inches, and measured values R = 2.25 inches and r = 0.75 inches.

3) For the above roll in (2), find the value of n when R is 1.5 inches (the outer radius in now 0.75 inches larger than r, but it started out as 1.5 inches larger than r). That is, use the d value from (2) to find the new n for the new R value.

4) For the above roll in (2), find the value of R when n is 223 (about half what it started out as). That is, use the d value from (2) to find the new R for the new n value.