Lenny Conundrum 316

[a_neezles_a]

The flagpole on the roof of the Chocolate Factory is 13 cm in diameter and a perfect cylinder. If one end of a 2300-cm-long string is attached to the top of the flagpole, and wraps around the flagpole exactly 16 times before ending at the bottom of the flagpole, how tall is the flagpole? Please round to the nearest centimetre, and submit only a number.

[shapu]

That's tough, but here's the thing:
If you look at the way the string travels, it actually creates right triangles as it goes down. 16 of them, in fact.

So the hypotenuse of each triangle is 2300 cm/16 (because it wraps around 16 times). One side of the triangle, the horizontal side, is 13*pi cm (because that's the wraparound distance).

Use your knowledge of the pythagorean theorem to figure out the height of each triangle.

That should get you started, but that won't completely answer the question.