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Thread: puzzle for all except darryl

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    opti-tipster harry a saake's Avatar
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    puzzle for all except darryl

    If you have a perfect cylinder tube, in which you can place three tennis balls end to end,how much empty space will be left over?

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    Rising Star
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    The rest of the universe

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    Master OptiBoarder
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    Counting the empty space inside the balls? :idea:

    I have no clue.

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    Objection! OptiBoard Gold Supporter shanbaum's Avatar
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    Quote Originally Posted by harry a saake View Post
    If you have a perfect cylinder tube, in which you can place three tennis balls end to end,how much empty space will be left over?
    Is this supposed to be a math quiz, or a test of reading comprehension?

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    Independent Problem Optiholic edKENdance's Avatar
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    i'm not certain but all of a sudden I crave Pringles.

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    Manuf. Lens Surface Treatments
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    Big Smile

    Quote Originally Posted by harry a saake View Post
    If you have a perfect cylinder tube, in which you can place three tennis balls end to end,how much empty space will be left over?
    in which you can.......................obviously you have not placed them yet.

    Therefore 100% is left over. :D
    Chris Ryser
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    OptiBoard Apprentice jimius's Avatar
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    Let's assume a tennis ball is 10 centimeter in diameter. This means the radius of the cilinder is 5cm, and it's height 30cm.

    Ball volume = 4/3 pi r^3 = 4/3 pi 5^3 = 261.8 cm^3
    261.8 cm * 3 = 785.4 cm^3

    Cilinder volume = pi*r^2*h = pi*5^2*30 = 2356.2 cm^3

    So space left = 2356.2 cm^3 - 785.3 cm^3 = 1570.9 cm^3 (or 66.6%)

    I hope i'm right :hammer:
    Someone stole my megahurtz!

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    One of the worst people here
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    I already passed the GMAT. No more math like this anymore for me.

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    Quote Originally Posted by jimius View Post
    Let's assume a tennis ball is 10 centimeter in diameter. This means the radius of the cilinder is 5cm, and it's height 30cm.

    Ball volume = 4/3 pi r^3 = 4/3 pi 5^3 = 261.8 cm^3
    261.8 cm * 3 = 785.4 cm^3

    Cilinder volume = pi*r^2*h = pi*5^2*30 = 2356.2 cm^3

    So space left = 2356.2 cm^3 - 785.3 cm^3 = 1570.9 cm^3 (or 66.6%)

    I hope i'm right :hammer:
    Sorry, but I get 4/3pi r^3 = 523.6 cm3^3 , hence

    space left = 2356.2 cm^3 - 3*523.6 cm = 785.4 cm^3 or about 33.3% left!

    You can also show that it is exactly 1/3 because you have

    h = 6r, cylinder volume: pi*r^2*6*r = 6 pi r^3

    i.e. space left = 6 pi r^3 - 3*4/3 pi r^3 = 2 pi r ^3 = 1/3 of cylinder volume

    (Always assuming there´s not a hidden secret in the exact interpretation of the question that we dont see )

    XW

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    OptiBoard Apprentice jimius's Avatar
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    Well, a "perfect cylinder" would be solid, so no balls would fit in at all.
    Also, math isn't my strong point. Just had to calculate a binoculiary field of view (or whatever it's called in english) in a multi-lens set-up. ugh.
    Someone stole my megahurtz!

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    opti-tipster harry a saake's Avatar
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    cylinder

    xiaowie from germany is the winner with the correct answer

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    Quote Originally Posted by harry a saake View Post
    xiaowie from germany is the winner with the correct answer
    Thanx a lot :D , I think the other poster just had made a slight typing error, but after that, I remembered from physics about packing ratios of spheres in crystal lattices and similar and thought it cannot be a coincidence that it´s almost 1/3, there must be a simple proof.

    BTW, I just noticed you are from Lake Norman, NC. Over the last years, I used to visits friends of mine pretty often in Davidson (some times twice a year) and know the Lake Norman area pretty well, especially around Cornelius. Where are you located? Maybe we can have a :cheers: next time?

    XW

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    opti-tipster harry a saake's Avatar
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    cornelius

    XW, yes, i would love to, actually i live in cornelius now, just about a mile off the lake, whereas i used to be right on the lake in mooresville, us two germans should get along well, you can e-mail me, private mail me or phone me at 704-763-9124:cheers:

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    Hey

    this german would like a :cheers: too

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    Quote Originally Posted by harry a saake View Post
    XW, yes, i would love to, actually i live in cornelius now, just about a mile off the lake, whereas i used to be right on the lake in mooresville, us two germans should get along well, you can e-mail me, private mail me or phone me at 704-763-9124:cheers:
    this german would like a :cheers: too
    GREAT, I will probably come abroad next spring, travelling from Chicago down to Charlotte. I´d love to get to House-ton to, but it´s a bit off track, i 4 (fear).
    I´d even bring original german :cheers: , however carying liquids on the airplane is a bit of a problem in the moment!:(

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