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Math Help - How many balls can fit into a jar

  1. #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 \pi6^{2}(24) = \approx 2,714.33605 and the volume of the balls which is \frac{4}{3}\pi1^{3} = \approx 4.1887902

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

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

    See Sphere packing, Kepler conjecture, and an attempt to construct a computer-verified proof.
    Thanks from daigo
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  3. #3
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    Re: How many balls can fit into a jar

    Quote Originally Posted by daigo View Post
    Does that number take into account the spaces between the balls when put into the jar?
    No.
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  4. #4
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    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.
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  5. #5
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    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!!
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  6. #6
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    Re: How many balls can fit into a jar

    Thank you for this answer this will make very easy.
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