A thick, flexible cable is wrapped by a machine very neatly and uniformly about a spool. The middle of the spool is a two-foot long cylinder. The diameter of the cylinder is two feet. It is known that when the cable has wrapped around the cylinder enough times to form a cylinder of diameter four feet, the length of that part of the cable is 1200 feet. Approximately what is the length of the cable that will fill up the spool, that is, will form a segment of a cylinder that is six feet in diameter and two feet long?
I got really stuck, is probably very easy I just can't see how to use the circumference and the cylinder at the same time.
If you assume that the length of cable is roughly proportional to the area of the circle bounding the annulus, with constant of proportionality $k$, then $$4^2k-2^2k=1200\implies k=100$$
Therefore the length of cable is $$6^2k-2^2k=3200$$