Balls in a Cube

[sqwash984]

So while working our team came upon a interesting problem. Stacking balls with in a volume and calculating this number, is alot harder than making a cube out of a ball and filling the volume, or just dividing volumes. I did a little research on keplers sphere packaging problem and found that the most efficient way to stack them is about 74% of their volume or if randomly places about 65% of their volume. Going by these numbers, assuming our robot is a storage containers 36x24x40 I can hold 390 balls at maximum efficiency and randomly placed it would be 343 at randomly designed. Is my math right and is there a better formula for this. My calc teacher couldn't direct me to a formula and I already asked them.

Tl;dr: How many balls can I fit into a cube that is 40x36x24 inches. And what is the math and how do I solve this. I found 74% max efficiency and 65% random efficiency.

Thanks