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# How many grains of sand in a cubic millimeter? Answered

I want to know how many grains of sand are in a cubic mm, because I want to work out how many grains of sand fit in my bedroom (using maths rather then filling it with sand and then counting for the rest of my life.)

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Sand grains vary in size significantly, depending on their source and any processing or sieving which was done to them. You can read the Wikipedia article on sand to find typical dimensions and compute a typical volume per grain; assuming a reasonable packing fraction (probably around 65% or so, see "sphere packing"), you can then work out the number of grains per unit volume.

The first sub-problem we need to solve is to figure out how many grains of sand there are in a volume of beach. We could measure this with any unit of volume we’d like—grains per cubic mile, grains per cubic kilometer, or whatever—but those would all be difficult estimates to make since they’re all really large volumes. And since the point of breaking the original problem up into sub-pieces is to come up with easier-to-solve problems, a better plan is to start by estimating the number of grains within a small volume—such as the number of grains per cubic centimeter.

How can we do that? Well, we can just gather up a bit of sand and count the grains. But instead of actually gathering a cubic centimeter of sand and counting each individual grain (which, while accurate, would also be tedious and slow), let’s make a quick and dirty estimate by lining up a bunch of grains in a row and measuring the length of the line in centimeters. The number you get will depend upon the type of sand, where it’s from, and a bunch of stuff like that—but if you do this you should get somewhere between 15 and 25 grains per centimeter (please email me and let me know what you get!). So if we assume that an average of 20 grains will fit along each side of a 1 cubic centimeter box of sand, we find that there are about 20 x 20 x 20 = 8,000 grains per cubic centimeter. Which, after a bit of fun converting units, we find is equivalent to 8,000,000,000 grains of sand per cubic meter.
- See more at: http://www.quickanddirtytips.com/education/math/how-many-grains-sand-are-earth%E2%80%99s-beaches?page=all#sthash.lUCmLW0t.dpuf

I understand this but how does this relate to my question?

"equivalent to 8,000,000,000 grains of sand per cubic meter. "

I assume you understood, but didn't read it all.

I didn't do this the information came from

http://www.quickanddirtytips.com/education/math/how-many-grains-sand-are-earth%E2%80%99s-beaches?page=all#sthash.lUCmLW0t.dpuf

ANY calculation is going to be an estimation unless your willing to fill the room and count it all. - even then if you did it twice you will get a different reading.

You HAVE to be realistic.

I didnt relise that was from a diffrent web site and because it was about a beach a practically ignored the rest of it sorry. I got it wrong.

I know but the way he worker out the amount of grains per centimeter was a bit of an estimation.

Duh. Did you read _any_ of the responses to this question? You _asked_ for an estimate, or are you too dense to realize that?

Sorry, I used the wrong words and I didnt understand what he ment at the time. My bad

Of COURSE its an estimation ! That's what we're telling you "sand" isn't a single entity, its shape varies.

Just a thought--- You won't be able to figure out how many cubic MM make up the volume of your room. First there is the fact that the walls are not perfectly square and also not parallel to the ground. The error factor of the construction it to large. Even adding extra taping compound to an area to cover up blemishes or even out the wall will change the volume of the room. The only true way would be to fill it with a volume of something that will not alter it (by pushing on the walls and causing them to bulge and then measuring the volume of that after you remove it.
Second, the volume of any furniture or other stuff will have to be accounted for. The volume of those would have to be removed from the total.
Finally, your putting a square peg in a round hole. There will be voids where the cubes don't fill completely because of the odd shapes. Those will add up and be yet another error factor.

I know but to be honest I am not too fussed about all that, I am just looking for an approximate figure.

...and there are more stars in the sky than grains of sand on all the beaches of the world.

Well, sort of....there are more stars in the Universe, but we can only see about a thousand or so in the sky ;-)

You've NO soul you haven't Kelsey.

SINCE you ARE being picky, its usually considered at around 6000 stars in both hemispheres, for someone with good vision in a dark location.

I used to have a soul, Steve. Then I went to grad school...

"good vision", "dark location", blah, blah, blah. I'm a city boy, Steve -- I'm lucky if I can see Venus, let alone anything else :-)