# 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 √ó 10-13 m3 and 4.85 √ó 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.

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16 years ago

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.

16 years ago

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.

15 years ago

(After a 10 month delay)… yes.

15 years ago

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.

Mike
15 years ago

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?

Monton
14 years ago

Hope this wasn’t your homework. Given: “one grain of sand has a volume of 1.3 * 10^-9 cubic feet (from gomath.com)” 1 cubic foot = 12 cubic inches 1.3×10^(-9) / 12 = 0.1083 x10^-9 cubic inches 2.54 cm per inch 0.1083×2.54 = 0.27516×10^-9 cm^3 one grain of sand has a volume of 0.00000000027516 cubic cm 1 cup = 8 oz 1 oz = 29.57 cm^3 8 * 29.57cm^3 = 236.56 cm^3 236.56 / 0.00000000027516 = 859,717,982,264.86 grains of sand or 8.5971798226486×10^11 in one cup.

14 years ago

Monton… 1 cubic foot = 1728 cubic inches, not 12.

SurfingTheEther
14 years ago

How far do you want to go? You might want to check out jamming. http://en.wikipedia.org/wiki/Jamming_(physics) Looks like this guy researches the stuff: http://cherrypit.princeton.edu/donev/

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