A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is tangent to every one adjacent to it. In the spaces between sets of four adjacent spheres, other...

A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is tangent to every one adjacent to it. In the spaces between sets of four adjacent spheres, other spheres rest, equal in size to the original. These spheres form in turn a second layer on top of the first. Successive lauers of this sort form a pyramidal pile with a single resting on top. If the bottom layer contains 16 spheres, what is the height of the pile in terms of the common radius r of the spheres.