i have a large spherical shell of diameter 30 cm. Find out the maximum number of small balls of diameter 2 cm that can be completely filled in the shell without any deformation?
This question has been bugging me for many days. i really don't have a clue about 3D configuration of balls inside the shell? how should i configure the balls to get maximum number of balls. please help me out solve this problem.
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Getting exact answers to packing problems is often hard because strange configurations can be more efficient than you would expect, but the corrections are small. You can start from the fact that the best packing density of spheres is $\frac \pi{3 \sqrt 2}\approx 0.74048$. Take the volume of the large sphere, multiply by this, divide by the volume of the small spheres and you have an upper bound to the number of small spheres. For a lower bound, put a small sphere on center, build a hexagonal close pack lattice, compute the distance of each sphere from the center, and count the ones that are within the large sphere. If those are close enough, you are done. Otherwise it is hard.
The problem of sphere packing inside a sphere is a research problem. You might take a look at the references at the Wikipedia page Sphere packing in a sphere. This being said, your ratio of the radii of the small sphere to the large shell is 1/15=0.0666..., which I don't think it is tractable with the current algorithms (although I might be mistaken). The approximation gives around 2500 spheres, while the algorithms have been run up to 200 spheres, so it's a long shot.