An Interesting Math Thingy

My friend Mike mentioned this one night:

Imagine a rope wrapped one time around the circumference of the earth at sea level. Now, if you add 6 feet to this rope (which is 131,259,849.6 feet long), how far about sea level will it be in order to accommodate that extra 6 feet?

Believe it or not, the rope will actually have to raise approximately 12 inches above sea level because of that extra 6 feet of rope.

The fine print:
Circ. earth = 131,259,849.6 feet
Dia. earth = 41,781,307.8 feet
Circ. earth plus 6 = 131,259,855.6 feet
Dia. earth plus 6 = 41,781,309.7
Dia. difference = 1.909 feet
Dia. difference divided by 2 = 0.954 feet / 11.46 inches