Billiard balls

A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. These balls form in turn a second layer on top of the first. Successive layers of this sort form a pyramidal pile with a single ball resting on top. If the bottom layer contains 16 balls, what is the height of the pile.

Correct result:

h =  39.6408 cm

Solution:

r=6.35 (2x)2=(6r)2+(6r)2 x2=18r2 x=18 r=18 6.3526.9408 h12+x2=(6r)2 h1=(6 r)2x2=(6 6.35)226.9408226.9408 h=2 r+h1=2 6.35+26.9408=39.6408 cm



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