SO, for some goofy reason a me and a guy I work with got into a discussion about how big a container 76 million grains of sand would fill… he says it would be several thousand pounds filling several large garbage cans while I contend it wouldn’t fill more than one small garbage can and weigh no more than 30-40 pounds. Any physics people out there that care to settle our debate?
You’re much closer in terms of volume. According to the Encyclopaedia Britannica, sand is
Using this range, a 1 meter cube would hold anywhere between 500,000,000 and 50,000,000,000 particles. The weight would depend on the the composition of the sand and how dry it is.
You might want to pick your arguments more carefully. The first thing we (or you) have to determine is Which sand? (As noted, you are generally closer, but your answer can still vary widely.)
There is “play sand” that comes in 50# bags to pour in your kid’s sandbox. There is a variety of “coarse sand” that is sometimes used in concrete applications, in lieu of play sand, where each grain can be 3 times the size (or more) of a grain of play sand. And there is “white sand” that is used in glass-making applications and aquariums where each grain is much smaller than the size of a grain of play sand. (We used to be able to get white sand for sandboxes, but too many kids’ eyes were getting cut up by grains of sand too small for the ER people to flush out, so they stopped selling it at nurseries and yard-and-garden stores.)
Choosing the correct variety of sand (and there are more than the three I mentioned) can radically alter the space that 76 million grains will take up.
Just to show that some of us are stranger than others, here are some rough calculations:
I am assuming Finnish dune sand, just because it came up first on Google. That gives us a mean grain diameter somewhere in the general vicinity of .27mm (splitting the difference in the listed grain sizes). Assuming cubical matrix packing (very inefficient, but you didn’t specify), that gives us
(.27mm)[sup]3[/sup]=.02mm[sup]3[/sup]
.02mm[sup]3[/sup]/grain*76000000grains
=1,500,000mm[sup]3[/sup]=.0015m[sup]3[/sup]
=.054ft[sup]3[/sup]=93in[sup]3[/sup],
which is roughly equivalent to a cube just over 4.5 inches on a side of very loosely packed sand. A SWAG at the weight (based on 1 cubic foot play sand sacks I’ve hauled about) puts it at about 10 pounds dry. If you assume dry coarse sand with equivalent packing, you can probably figure on 1 cubic foot and around 25-30 pounds.
Enore, it looks to me like the general consensus is that your coworker is hopelessly off, while you merely overestimated slightly. If you tweak my numbers by assuming the right kind of sand and the right size garbage can, you can still come out of this pretty close to right. I don’t suppose there’s a bet riding on this, is there?
Now, let’s watch the real math and physics people take this apart–with luck, it’ll degenerate into a discussion of efficient packing algorithms within a few hours, and my errors in assumptions, calculations, conversions, and physics will be forgotten.
You people scare me.
Seriously, I am SO impressed by people who can use numbers containing more than two zeros, since I am profoundly dyscalculiac.
Please return to your regularly scheduled thread. 
Just out of curiosity, why 76 million?
–sublight.
At a guess: since the optimum packing density of identically sized spheres is roughly 76% solid to 24% voidage. You could then do the sums for 100 million perfect cubes.