Number+Three

A snug-fitting belt is placed around the Earth's equator. Suppose you added an extra 1 meter of length to the belt, held it at a point, and lifted until all the slack was gone. How high above the Earth's surface would you then be? That is, find h in the diagram below. Assume that the Earth is a perfect sphere of radius 6400 km, and that the belt material does not stretch. An approximate solution is acceptable.