Imagine that you have perfect sphere the size of the Earth. Around its equator is a piece of string, tight to the sphere so there is no gap and joined it such away that it is perfectly smooth (no knots, bumps etc). You cut the piece of string and then insert another piece just 3ft long which is again joined so the joint is smooth. The resultant new circle of string is positioned so that it shares the same centre as the sphere i.e. so that there is a uniform gap between string and sphere all the way round (looking from above you would see two concentric circles. What order of magnitude would you think the gap between sphere and new circle of string would be? Is it, for instance, going to be so small that you can't see it easily, or what?
Most people will be able to do the maths on this puzzle and I think you will be surprised at the answer!
Maths is posted below:-