Helix (spool and wire) geometry

[Sierpinski]

Homework Statement

(From Stewart's Calculus Early Transcendentals (4th ed), Ch. 13 Problems Plus #8)

A cable has radius r and length L and is wound around a spool with radius R without overlapping. What is the shortest length along the spool that is covered by the cable?

Homework Equations

See image link below.

The Attempt at a Solution

I've read the solution from the solutions guide and it makes sense, aside from this geometric representation:
(h=vertical distance between coils)

http://img242.imagevenue.com/img.php?loc=loc164&image=th_34593_spool2_122_164lo.jpg"

I'm trying to understand the rationale for this geometric image. Specifically, where is the 2Pi(R+r) coming from? This is clearly the circumference of the spool/cable, but I don't understand its presence in the image. Could someone describe what the image is showing (where the spool is, how it's oriented, what the two parallel line are, etc)? Thanks!

http://img107.imagevenue.com/img.php?image=35205_spool_122_371lo.jpg"

 

[Sierpinski]

I thought I would repost the image, as the link above has too many ads.
Any ideas?