SOLUTION: How do I calculate the number of 1.38 cu in spheres can be put into a drum that is 21" diameter and 29" high?

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Question 883942: How do I calculate the number of 1.38 cu in spheres can be put into a drum that is 21" diameter and 29" high?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The quickest way to calculate is to divide the volume of one sphere into the volume of the drum.
N=%28pi%2A%28D%2F2%29%5E2%2AL%29%2F%281.38%29=%28pi%2821%2F2%29%2829%29%29%2F1.38=7278
Although quick it is inherently incorrect and overestimates the number because it doesn't account for gaps in between the spheres which normally exist.
If you think of how cannonballs are stacked and do something similar with these spheres, the maximum density you can achieve is pi%2F%283sqrt%282%29%29%2AV%5Bmax%5D or 0.741%2AVmax
So the maximum number would decrease to 5389.
For more information, look up close packing or center packing of spheres in your favorite search engine.