Question

Really weird question, please help! Thank You!

A chef makes Chinese Noodles. He first makes a rope of dough(roughly circular cross section, treat as circular) 5.0 cm in diameter. He then doubles the rope on itself (making 2 ropes out of the original rope), repeating (making 4 ropes, etc.). What is the thickness of the original noodle if he folds the noodles 20 times.

Thank You! This question has me stumped!

Answer 1

@triciaal @johnweldon1993 @jabez177 @jim_thompson5910 @SolomonZelman @zepdrix @tkhunny @whpalmer4

Answer 2

So let me figure what this question is even asking! It's a bit tricky in wording.
So when the chef doubles the rope, what affect does that have on the diameter of the rope? I'm thinking dividing in half?

Answer 3

I agree with @neonumbrella5115

the first original rope has a circular cross section with diameter 5 cm
then you cut the rope in half, maybe along this line shown here



so you'll now have 2 ropes with circular cross sections of diameter 5/2 = 2.5 cm

repeat and you'll go from 2.5 to 2.5/2 = 1.25

etc etc

Answer 4

You'll notice the diameters follow a geometric sequence, so you can use this formula

\[\Large a_n = a*r^{n-1}\]

in this case, a = 5 is the original starting diameter and r = 1/2 = 0.5 is reflecting the fact that you cut the diameter in half over and over

Answer 5

oh I see

Answer 6

but wouldn't I need to use an equation for cylinders to solve it?

Answer 7

@neonumbrella5115 yea, I think it divides in 1/2

Answer 8

@jim_thompson5910 I wonder about this answer (and the problem in general). If you have a cylinder with diameter \(d\) and length \(l\), the volume is \[V = \frac{\pi}4 d^2l\]If you then stretch it to make it twice the length with constant volume, \(d\) changes by a factor of \(\sqrt{2}\), not a factor of \(2\).

I think this is an example of someone trying to fit a math concept to a real-world item and not doing a good job. The noodles in question are flat, not round. Here's a video showing them being made, note that the process of this problem starts at about the halfway point in the video. https://www.youtube.com/watch?v=JyNN3heu6nM