How many balls can fit into a jar

The jar has a radius of 6" and a height of 24" and each ball has a radius of 1".

So I found the volume of the jar which is and the volume of the balls which is

And then I divided how many of the balls can go into the jar by dividing:



Does that number take into account the spaces between the balls when put into the jar? Like the small gaps when spheres are placed next to each other.

See Sphere packing, Kepler conjecture, and an attempt to construct a computer-verified proof.

Quote:

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Originally Posted by daigo

Does that number take into account the spaces between the balls when put into the jar?

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No.

Yeah, you need to take into account the packing density, and the fact that it is not 1. Read emakarov's link to sphere packing.

The 648 balls will fit IF you use a "ball grinder" on each,
grinding them to dust!!

Thank you for this answer this will make very easy.