[KRuchan]

Maybe I am missing something here, but why is 1 a neat problem? You are increasing the radius by 1 meter so the length of the band is now 2pi(r_e + 1) making the increment 2*pi meters. Is the surprisingly low increment the point of the problem?

[Jun8]

Most people when faced with 1 and knowing the huge circumference of the Earth estimate (using Sytem 1 type thinking, http://en.wikipedia.org/wiki/Dual_process_theory#System_1) it would be longer by kilometers.

[JoshTriplett]

Yes, exactly; if you don't start out by doing the math, the result can seem unintuitive.