How many grains of sand fill a 10-litre bucket?

Question

Take a typical grain of sand to be about half a millimetre across, and a bucket holding 10 litres. Solve in your head. Estimate how many grains of sand fill the bucket. Aim: under 60 seconds.

Accepted Answer

Put both volumes in the same units. Bucket: 10 L = 0.01 m^3. Give each grain its own tiny cube of side 0.5 mm = 5 	imes 10^{-4} m: (5 	imes 10^{-4})^3 = 125 	imes 10^{-12} = 1.25 	imes 10^{-10} 	ext{ m}^3. Divide: \frac{0.01}{1.25 	imes 10^{-10}} = \frac{10^{-2}}{1.25 	imes 10^{-10}} = 0.8 	imes 10^{8} = 8 	imes 10^{7}. That is on the order of 100 million grains (a defensible range of 50–150 million, since grain size varies and real grains pack with gaps). Takeaway. The answer is brutally sensitive to the grain size because volume scales as the cube of the diameter, halving your assu…

How many grains of sand fill a 10-litre bucket?

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