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July 8th, 2012, 09:16 AM   #1
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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 and the volume of the balls which is

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



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.
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July 8th, 2012, 10:12 AM   #2
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Re: How many balls can fit into a jar

648 is correct IF each ball is melted into a liquid.

Before you go nuts with this, google "packing identical spheres in a cylinder"...
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July 8th, 2012, 10:47 AM   #3
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Re: How many balls can fit into a jar

Hello, daigo!

Quote:
The jar has a radius of 6" and a height of 24", and each ball has a radius of 1".
How many balls can fit into the jar?



And then I found how many of the balls can go into the jar by dividing:
[color=beige]. . . [/color]

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?[color=beige] . [/color] [color=blue] . . . No[/color]

You have melted 648 balls.
[color=beige]. . [/color]Then you poured the liquid into the jar.
You have filled the jar with the equivalent volume of 648 balls.

If we leave the balls intact, the problem becomes difficult.

We can arrange the balls like this on the floor of the jar.

[color=beige]. . [/color]

Then we can place 6 more balls around them
[color=beige]. . [/color]and have a large hexagon of 13 balls.
These will fit inside the jar.

These layers are 2 inches high.
We can fit 12 such layers in the jar.

Hence,




I'll let you work out the details . . .

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