# number of gumballs

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• Jul 26th 2011, 09:04 AM
Veronica1999
number of gumballs
A spherical globe, 12 inches in diameter, is filled with spherical gumballs, each having a one inch diameter. Estimate the number of gumballs in the globe, and explain your reasoning.

The volume of the globe is 904.32 and the volume of each gumball is 0.523333.
This allows 1728 gumballs to fit in the globe.
This doesn't seem right.
• Jul 26th 2011, 09:33 AM
TheChaz
Re: number of gumballs
There is "dead space" (i.e. just air) in between gumballs. If they were somhow liquified, then we could just divide the total volume (~900) by the volume per gumball (~.5) to get ~1800.

One approach would be to take a rough average between our first guess (1800, or 1728...) and the following:
Imagine 1 (in^3) cubes. We could fit ~900 in there, so the average would be around 2350.
• Jul 26th 2011, 12:37 PM
CaptainBlack
Re: number of gumballs
Quote:

Originally Posted by Veronica1999
A spherical globe, 12 inches in diameter, is filled with spherical gumballs, each having a one inch diameter. Estimate the number of gumballs in the globe, and explain your reasoning.

The volume of the globe is 904.32 and the volume of each gumball is 0.523333.
This allows 1728 gumballs to fit in the globe.
This doesn't seem right.

Kepler problem/conjecture/theorem?

Its consequence is that the maximum packing density of spheres is ~74%.

In this case you will not be able to obtain this because of the finite volume of the container and the irregularity of the packing. Experimental results for random close packing give a maximum of ~50% and theory says that random close packing cannot exceed about 64%.

CB