What volume does 1 million grains of sand occupy?

Question

on average?

Answer 1

That would be a cube 100 grains high, wide and deep.

Volume depends on the size of the grains. If each grain is 1/30 inch (in the coarse-grained sand range), each side of the cube will be 3 1/3 inches in length. That's a volume of about 37 cubic inches.

If the sand is in the fine sand range, maybe 1/300 inch, the sides of the cube will be 1/3 inch, and the cube will be 0.037 cubic inch.

For most sands you can get a million grains in a coffee cup with room to spare.

Answer 2

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The diameter of a sand grain is from 2 millimetres right down to one-sixteenth of a millimetre, in five steps of a factor of two each time through very coarse, coarse, medium, fine, and very fine. Anything coarser is called "gravel", and finer is called "silt". For the medium sand from a quarter to a half millimetre, a million grains will form into a cube with sides from from 25 millimetres to 50 millimetres, which is very nearly from one inch to two inches. But the very finest sand would only be a quarter-inch cube, and the very coarsest a huge eight-inch cube, so there is a larger possible range than you were probably expecting.

Answer 3

It's a range, anywhere from 31.1 cubic inches (510 cc) down to a tiny 0.0616 cubic inches (1 cc).

According to the Wentworth Scale of grain size, "sand" can be anywhere from 0.039 inches to 0.0049 inches in diameter.

If we assume that the grains are poorly packed (because I don't want to do the math for good packing), then you have, volume of a sphere, minimum radius

V = (4/3) * π * r^3
V = (4/3) * π * (0.0195 in)^3
V = (4/3) * π * (7.41E-6 in^3)
V = 3.1059E-5 in^3

So one million of them

Vt = (1,000,000) * (3.1059E-5 in^3)
Vt = 31.1 cu in

Maximum

V = (4/3) * π * (0.00245 in)^3
V = (4/3) * π * (1.4706E-8 in^3)
V = 6.16E-8 in^3

Vt = (1,000,000) * (6.16E-8 in^3)
Vt = 0.0616 cu in