# Thread: How many balls can fit into a jar

1. ## 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.

2. ## Re: How many balls can fit into a jar

See Sphere packing, Kepler conjecture, and an attempt to construct a computer-verified proof.

3. ## Re: How many balls can fit into a jar

Originally Posted by daigo
Does that number take into account the spaces between the balls when put into the jar?
No.

4. ## 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.

5. ## 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!!

6. ## Re: How many balls can fit into a jar

Thank you for this answer this will make very easy.