# Basic Conundrum

1. Jun 24, 2009

### cc_blue_cc

The flagpole on the roof of the 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.

2. Jun 24, 2009

### VeeEight

You must show your attempt if you desire help. Have you tried the usual stuff like drawing a picture or looking at your notes for something relevant?

3. Jun 25, 2009

### Staff: Mentor

One technique that comes to mind is to find the equation(s) of the curve in space along which the string lies, and then find the arclength of that curve. This technique requires the use of calculus, which is probably inappropriate for a question posted in the Precalculus Math forum. On the other hand, newbies often post their questions to the wrong forum, so maybe this technique is applicable.

Assuming that's the case, the parametric equations for the curve that represents the string are
x = 6.5cos t
y = 6.5 sin t
z = Kt

where 0 <= t, and K is a constant that needs to be determined so that if the string is wrapped around the pole 16 times it reaches the top of the pole.

4. Jun 25, 2009

### Avodyne

There is a much easier way to do this problem.

5. Jun 25, 2009

### cepheid

Staff Emeritus
No kidding! That's exactly what I was thinking...

6. Jun 25, 2009

### Staff: Mentor

Well, hey, if your only tool is a hammer, everything looks like a nail!

An easier way would be to "unroll" the flagpole and see how far 1/16 of the string reaches. Did you have in mind something like this?

7. Jun 30, 2009

### The_Doctor

Draw the net of the flagpole, and where the string would be. You will need pythagorus theorem.