Imagine the earth as a polished metal sphere with a steel band around the equator flush against the surface.
The band is cut and one foot added to its length. It's then rewelded together and positioned so as to be equidistant from the surface of the sphere (still at the equator) all the way around.
How much space would there be between the band and the surface of the sphere? Enough to slip a playing card maybe?
How about if the sphere were not the size of the earth but the size of the sun instead? Or the galaxy? Or a baseball? How much space between the band and the surface of the sphere then?
Solution to Earth Band Puzzle
The exact amount of space is about 1.9 (or 6/π) inches and is the same no matter how large or small the sphere the band is around. You can figure out the problem with grade-school algebra and observe that the radius of the sphere just cancels itself out.