Little Euclid was playing with a cuboidal box, with a square base, and 14 identical wooden spheres. He observed that he could snugly and perfectly layer comprising three rows and three columns. He then placed another layer of four spheres, stably sphere in the second layer touched exactly four spheres of the bottom layer. Finally he placed the last sphere, stably and symmetrically, on top of the second layer and observed that he could then just close the lid of the box. Find the ratio of the height of the box to the radius of each sphere