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How many grains of sand can fit into one cup?

I cannot find the answer anywhere on the web. Here are some hints:

  • one grain of sand has a volume of 1.3 * 10^-9 cubic feet (from gomath.com)

  • Some people on abc.net.au tried to figure out how many grains of sand are on earth.

  • Hypertextbook.com says the volume varies between 1.13 × 10-13 m3 and 4.85 × 10-9 m3

  • There's a group of 13 people that spent 1,000 hours counting 3,281,579 grains of sand. There's a photo on their webpage at multiply.com.
Okay smartypants, if anyone out there can find the answer to how many grains of sand fit into one cup volume, then you are the first person ever to figure that out.


Posted by: spudart on Sep 21, 07 | 5:00 am | Profile
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Sounds like a math problem to me. Don't you have the information you need right here? If you know the size and volume of a grain of sand and the volume of a cup, I think you could figure it out, But then again I'm no math genius.

Posted by: Tom on Sep 21, 07 | 7:19 am


Using the volume of 1.3 * 10^-9 cubic feet - you would need 7692307.69 grains of sand to fill one cup. (rounded to 2 significant digits)

The range of 1.13 × 10^-13 m3 and 4.85 × 10^-9 m3 is a pretty huge range. The smallest volume would require 2097345132.74 grains, the largest 48865.98 grains.

Posted by: sparx on Sep 24, 07 | 6:51 pm


so between 48,000 and two billion grains?

Posted by: spudart on Sep 24, 07 | 10:40 pm


(After a 10 month delay)... yes.

Posted by: sparx on Jul 16, 08 | 4:45 pm


I am sorry. That range is just unacceptable. I need the answer within a range of one hundred thousand grains, not 1,999,952,000 grains.

Posted by: spudart on Jul 16, 08 | 5:12 pm


Then you need to specify the size of the grain of sand.

But.. using the size given by gomath, the answer is 7,692,308 grains.

Posted by: sparx on Jul 16, 08 | 6:11 pm


let's say the grain of sand is spherical. Would we need to take into account the spacing between each grain. I know it might be insignificant but lets say for example I wanted to know how many Jelly beans are in a cup. Wouldn't that have impact on the accuracy of the true result?

Posted by: Mike on Nov 06, 08 | 12:04 pm


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Hi. I'm Matt Maldre. Every single weekday my blog on spudart.org has a new post with an original idea or discovery. Be sure to stop by daily to see what's happening.



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