jc wrote:I would like to place 8million 1 millimeter beads in a baby bottle. How large would the bottle have to be to contianthe beads?
It would have to be a big, strong baby to lift the bottle. I get about 5.66 L.
You may wish to read the Wikipedia article on "close packing" (Google for it)
The volume of one sphere is (4*pi/3)*rÂ³ or (pi/6)*dÂ³, using the diameter.
In an optimium lattice structure, close-packed spheres will occupy pi/sqrt(18) of the volume. This is only true for the lattice shape and any practical package will have minor errors at the walls (as long as minimum dimensions are several times the sphere dimension).
Thus (pi/sqrt(18))*Vc = (pi/6)*n*dÂ³
and Vc = (0.5*sqrt(2))*n*dÂ³
This is 4*sqrt(2)*10^(-3) mÂ³ or 4*sqrt(2) liters. While this evaluates to 5.6585. . . liters, I would recommend rounding up at least to 5.66 L to allow for wall effects.