



 
Jeff, Rather than trying to draw a diagram I just took a paper towel roll cut it along the spiral seam and rolled it out flat. (there is a change of scale in the two photos.)
I then added some lines and labels. The side ED was extended to G so that angle BGD is a right angle. This makes the length BG equal to the height of the tube which I am going to call H. In your problem H = 102 inches. Triangle ABC is a right triangle, AC = W is the width of the paper (in your example W = 3 inches) and AB = C is the circumference of the circular end of the roll (in your example C = π × diameter = 2π inches). Triangle DBG is also a right triangle and since ED and AB are parallel angles ABC and GDB are congruent. Thus triangles ABC and DBG are similar. Hence
You know the values of C, W and H and hence you can find BD. The length of the paper strip required is BD + EF. But EF is the side of a right triangle with the hypotenuse of length C and the third side of length W and hence you can use Pythagoras theorem to find EF. I hope this helps,  


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