Good calculations, but perhaps a bit too complex.
Here is a simpler one, which provides almost exact results (based on the example at the bottom).
If the inner and outer diameters are D0 and D1, then calculate the cross-sectional area of the roll as follows (where r1=D1/2 and r0=D0/2):
Pi * (r1^2 - r0^2)
Now simply divide this by the thickness h.
Using the numerical example on this page,
approximate formula roll length: 235.4623694 m
exact formula roll length: 235.6194545 m
this formula: 235.619449 m (which matches the exact formula to 7 digits).
Cheers,
Pranab