which uses/wastes more space?

Question

say i had two identical jars. say i filled one jar with 1inch balls, and the other jar with 2 inch balls. which jar would have more empty space in it, meaning.. inbetween the balls there will be space.


secondly, as a general rule, is there more empty space with using larger or smaller balls?

Answer 1

There is more emPty space using large balls

Answer 2

if you packed them in the most efficient way possible, i think both would have an equal amount of empty space. i just looked it up on wikipedia, which says that the greatest density occupiable by the spheres is 0.74048 http://en.wikipedia.org/wiki/Close-packing_of_spheres

that's a constant, so the volume of empty space is constant as well

say the jar is packed with 1 inch balls, and that 0.26 of the jar is empty space

if you were to magically double the radius (or diameter) of the balls, the volume would be increased 2*2*2 = 8 times

only 1/8 of this new volume would fit into the jar

and as for the empty space, the new total empty space would be 8*0.26 of the jar, but that doesn't fit in the jar either, only 1/8 of it does

so 8*0.26 * 1/8 cancels out to give 0.26 again

thus, still 0.26 of the jar is empty space



note about comparing with sand: even though you can't see it, there is a lot of empty space in sand. you know how easily water can fit in sand? there's lots of tiny spaces in there, and it probably would give the same amount of empty space as 1-inch balls

Answer 3

The first jar that is the jar filled by 1inch balls would have more space as the balls are spherical they touches each other at only one point and other space between them remain empty. in general, smaller balls creats more space than the larger.

Answer 4

There is actually no difference between the two if you only consider spheres packed together and don't worry about where they touch the sides of the container.



The situation with the bigger spheres is only an enlargement of the situation with the smaller ones. There are bigger spaces between the large spheres but this is balanced by the fact that they occupy larger solid space themselves.



Spheres of any size packed together will use up the same percentage of available volume which is pi/sqrt18 = about 74%. Once again I emphasise that this only applies to speres packed together without limitation.

Answer 5

The larger balls take up more space & leave bigger air spaces

Consider the difference between a square of 2" sides & the 2" dia ball

Answer 6

There will be more wasted space with the larger balls.



The smaller balls can be packed tighter.



To realise this, picture balls as small as grains of sand

There would then be hardly any wasted space.



This would be a general application.