How Much Extra Rope is Needed to Raise it One Meter Above the Earth?

[kash25]

I'm collecting some data for school and need data from as many people as possible. Thanks!

Who can solve this problem in one try without looking at the answer?A fool wants to tie a rope around the earth. So he buys a rope of 40,000 KM and ties it around the world. His neighbour, also a fool, wants to do the same only he wants the rope on sticks 1 meter above the ground.

How much more rope does he need?

And how much more rope do you need when you use a tennis ball instead of the earth?Be honest! And be sure to leave a post saying whether or not you get it on the first try!

The answer can be found at http://mindcipher.com/puzzle/42-don-t-hang-yourself

Thanks for your help!

 

[qntty]

If the circumference of the Earth is 40,000 then the radius is $\frac{20000}{\pi}$. So the circumference in the second instance is $2 \pi \left(\frac{20000}{\pi} + \frac{1}{1000}\right) = 40000 + \frac{\pi}{500}$. Obviously a tennis ball would be the same thing. That was my first try.

 

[adriank]

He needs an extra $2\pi$ metres of rope, regardless of the radius of the object it was wrapped around.

First try, although I have seen this problem before. (I got it the first try then as well.)I believe that even if you wrap the rope around a non-circular object (with reasonable restrictions; using a convex object will suffice), you would still have to add $2\pi$ metres to make each point on the rope 1 metre from the object.

 

[Office_Shredder]

We actually had a discussion on this after a math society meeting (I've seen the question before and answered it on my first try for the record). 9 out of 10 university students were able to get the answer right on the first try, the 10th took 10 minutes of explaining because "your notation is stupid"