How many balls can fit into a jar

• Jul 8th 2012, 08:17 AM
daigo
How many balls can fit into a jar
The jar has a radius of 6" and a height of 24" and each ball has a radius of 1".

So I found the volume of the jar which is $\displaystyle \pi6^{2}(24) = \approx 2,714.33605$ and the volume of the balls which is $\displaystyle \frac{4}{3}\pi1^{3} = \approx 4.1887902$

And then I divided how many of the balls can go into the jar by dividing:

$\displaystyle 2714.33605 \div 4.1887902 = 648 balls$

Does that number take into account the spaces between the balls when put into the jar? Like the small gaps when spheres are placed next to each other.
• Jul 8th 2012, 08:50 AM
emakarov
Re: How many balls can fit into a jar
See Sphere packing, Kepler conjecture, and an attempt to construct a computer-verified proof.
• Jul 8th 2012, 07:34 PM
Wilmer
Re: How many balls can fit into a jar
Quote:

Originally Posted by daigo
Does that number take into account the spaces between the balls when put into the jar?

No.
• Jul 8th 2012, 08:30 PM
richard1234
Re: How many balls can fit into a jar
Yeah, you need to take into account the packing density, and the fact that it is not 1. Read emakarov's link to sphere packing.
• Jul 8th 2012, 09:47 PM
Wilmer
Re: How many balls can fit into a jar
The 648 balls will fit IF you use a "ball grinder" on each,
grinding them to dust!!
• Jul 18th 2012, 04:36 AM
kraj8995
Re: How many balls can fit into a jar
Thank you for this answer this will make very easy.