Rope length puzzle
Case A: Imagine you have a rope tightly wound around a basketball. How much more rope do you need for the rope to be one foot away from the surface of the basketball at all times? (as if it is tightly wound around an imaginary ball that has radius one foot more than the radius of the basketball). I do not need an exact answer now. Just imagine it.
Case B: Now imagine you have a rope tightly would around the equator of the earth (what, about 25,000 miles or so?). How much more rope do you need for the rope to be one foot away from the equator at all times? (as if the radius of the earth had increased by a foot). I do not need an exact answer now either. Just imagine it.
Now for the puzzle:
In which case do you think you need more rope – Case A or Case B? Any rough idea by how much?