Length of wire wrapped spirally around a cylinder I am not able to approach this question:
A thin copper wire is wound, uniformly and spirally, in a single layer, from the bottom to the top, around a cylindrical iron rod. The circumference of the iron rod is 2 cm. and its height is 56 cm. If the number of turns in the spirally wound copper wire is exactly 45, what is the length of the copper wire used?
Can somebody help me get through this?
 A: Get yourself some superthin transparent paper rectangle of height $56\,\mathrm{cm}$ and width $2 \cdot 45\,\mathrm{cm}$.
Draw the diagonal of this rectangle and wrap the paper aroud the cylinder. The diagonal line matches the wire exactly and is how long?
A: I think you can use the Pythagorean theorem for this. Imagine wrapping the wire around exactly one time out of the $45$ wrap-arounds yet to come. The height difference between where the wire started at the base of the cylinder and where it stops is exactly $\frac{56}{45} \text{cm}$. Now hold the wire down at the base and unwrap the rest of the wire until until it is straight, making sure that the wire does not change height at any point during the unwrap process. Now perceive this straight length of wire as the hypotenuse of some triangle. You know the height already, and the base of the triangle will be just the circumference of the cylinder. You have enough information to solve for the length of the wire now. If you were to repeat that process $44$ more times you'd have the length of wire that you seek as an answer to  this question. In other words, multiply the length of the hypotenuse of this triangle I suggested by a factor of $45$ and you'll have your answer.
