Grains of Sand v Humans

[stegosaurus]

How big a cube would you need for there to be as many grains of sand contained within as there are humans on the planet?

[magicdice]

let's assume a grain of sand is roughly spherical, and 0.5mm wide (at a guess). this means the volume of one grain of sand is roughly 5.236x10^-10 m�

population of the world, according to these guys at the time of me answering this is 6,432,430,625

so total volume is 6,432,430,625 x 5.236x10^-10

that comes to 3.37m�, which is less than the total volume of a smart car.

[kempie]

Following on from magicdice

we have a cube containing approx. 6.4 billion grains.

each side of the cube would be approx. 1860 grains in length.

sand is defined as 'a sedimentary material with grains between 0.06 and 2.0 millimeters in diameter'.

thus the height of the cube would be anywhere between 111.6 and 3720 mm (0.1116 and 3.72 metres)

[brachiopod]

Aah, but you have to take into account the packing of the grains.

magicdice, in calculating the volume of a grain of sand, and multiplying this volume for X billion grains of sand, you are not taking into account the interstices (ie the 'space between the grains' which would obviously increase the volume from that calculated.

kempie, though your reasoning is excellent, you've gone the other way a bit. In that, for a grain size of diameter d, the length of side of a cube of 6.4 billion grains would be slightly less than 1860d .

The grains would not lie on top of each other 'end-to-end' as such, but would lie in the gaps between the grains in the layer below.

As an analogy, (and since the snooker is on) - if I placed the cue ball on top of the reds in the triangle before the break, the cue ball would lie in one of the 'gaps' between three reds, and would not lie directly on top of a single red. Thus the height of the two layers of balls would be less than twice the diameter.

In 'ideal' ordered structures, (crystal lattices and the like), these 'packing' arrangements occur as either hexagonal close-packing or cubic close-packing systems, depending on exactly where the third layer lies!!

[kempie]

As my original post indicates such a wide range in the possible answer I just couldn't be bothered to factor in such variables as

• grains not being a perfect sphere
• not being identically sized
• not forming perfect HCP, Face-Centred Cubic, Body-Centred Cubic or other lattice structure
• not knowing the exact human population of the world at any given moment

but perhaps I should have mentioned that the factors exist.  My bad.

[Skids]

Dunno, but it would take the same amount of people to fill the volume of the sun as there are atoms in the human body.

[newtron]

Adjusting magicdice's volume estimate for porosity, as suggested by Brachiopod is easy as the porosity of sand typically ranges between 25 and 50%.  So assuming the porosity is 35%, the total volume would be approximately 5.18m�.