Originally Posted by pdurrant
Call the Earth's radius r feet. The string length around the world is τr feet. (Where τ is 2π.)
Add 10 feet. New string length is τr+10. Radius of new circle with circumference τr+10 is (τr+10)/τ = r+10/τ.
So it will be 10/τ feet above the surface. That's about 1.6 feet.
See, I knew pi was in there somewhere