Which weighs more, a cubic meter of large sized coal or a cubic meter of small sized coal (assume that all the pieces of coal in each cubic meter are loosely packed identical-sized spheres, each sphere touching six others)?

sequoianoir

I think they are both the same. (if we are talikg about a 1 metere cube - not exactly the same as 1 cubic metre) If you put a sphere (diameter 2) inside a cube (size 2 x 2 x 2) the sphere is a perfect fit (touches all sides) but there is obviously some 'wasted space'. This 'waste' is the same percentage as a sphere (dia 1) in a cube 1 x 1 x 1. The cube 1 x 1 x 1 would fit 8 times in the cube 2 x 2 x 2. So 8 spheres (dia 1) fit in the cube 2 x 2 x 2. Both cases have the same amount of 'waste' space. So providing the coal is spherical it should make any difference ! Dec 09 02, 7:52 PM

Gnomon

Given the very artificial conditions outlined in the question, the two cubic metres of coal will way the same. Dec 09 02, 8:35 PM

Friar Tuck

You can put one 1 metre diameter sphere inside a cubic metre and the volume of the sphere would be (pi x 1 x 1)/4 = 0.25pi. You can put eight 0.5 metre diameter spheres in the same space and their volume would be ((pi x 0.5 x 0.5/4) x 8 = 0.5pi so therefore the small pieces have the greater volume and therefore the greater weight. Dec 09 02, 8:38 PM

sequoianoir

Sorry Friar Tuck but you got it totally wrong ! Formula is Four thirds Pi radius cubed. Volume = ( 4 x PI x R x R x R ) divided by 3 Since the 4, Pi and the 3 is constant then the relative volumes of 2 different size spheres is the variable called diameter If diameter = 1 then radius is 0.5 and relative volume 0.5 x 0.5 x 0.5 = 0.125 If diameter is 0.5 then radius is 0.25 and the relative volume is 0.25 x 0.25 x 0.25 = 0.015625 8 x 0.015625 = 0.125 THE SAME !!! Dec 09 02, 9:07 PM