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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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?
The rest of the universe
Counting the empty space inside the balls? :idea:
I have no clue.
Is this supposed to be a math quiz, or a test of reading comprehension?Quote:
Originally Posted by harry a saake
i'm not certain but all of a sudden I crave Pringles.
in which you can.......................obviously you have not placed them yet.Quote:
Originally Posted by harry a saake
Therefore 100% is left over. :D
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:
I already passed the GMAT. No more math like this anymore for me.
Sorry, but I get 4/3pi r^3 = 523.6 cm3^3 :confused: , henceQuote:
Originally Posted by jimius
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 :nerd: )
XW
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.
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.Quote:
Originally Posted by harry a saake
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
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
Quote:
Originally Posted by harry a saake
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).Quote:
this german would like a :cheers: too
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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