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Thread: Only for real math pros!

  1. #1

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    transcendental analytic kedaman's Avatar
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    An upside down cone with diameter 10m and height 8m is being filled with water, 0.1 m^3 per minute.

    What's the speed the surface raising when the water height in the cone is 4 meter
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    writing software in C++ is like driving rivets into steel beam with a toothpick.
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  2. #2
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    I make it (48/(250*pi)) * ( ( 192 / (25*pi) )^(-2/3) ) /60
    = 5.61296766986877E-04 m/s

    about half a centimetre per second

  3. #3

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    transcendental analytic kedaman's Avatar
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    Hey, I got 2.12E-5 m/s
    That's 21 micrometers per second, about 1,2 millimeters/s

    Something must have screwed up, either you or me or both got wrong answers, so

    did you get this equation for height?
    h=2t/(625pi)^(2/3)
    and then got the derivate and put in t in it?
    I got t=20000pi seconds for h=4
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    writing software in C++ is like driving rivets into steel beam with a toothpick.
    writing haskell makes your life easier:
    reverse (p (6*9)) where p x|x==0=""|True=chr (48+z): p y where (y,z)=divMod x 13
    To throw away OOP for low level languages is myopia, to keep OOP is hyperopia. To throw away OOP for a high level language is insight.

  4. #4

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    transcendental analytic kedaman's Avatar
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    838 m^3 should go in the cone, and if you fill it 0,1m^3 /minute, should take up nearly six days to fill
    Use
    writing software in C++ is like driving rivets into steel beam with a toothpick.
    writing haskell makes your life easier:
    reverse (p (6*9)) where p x|x==0=""|True=chr (48+z): p y where (y,z)=divMod x 13
    To throw away OOP for low level languages is myopia, to keep OOP is hyperopia. To throw away OOP for a high level language is insight.

  5. #5
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    my bad, I missed out a couple of constants
    I got 2.97001026127106E-04 m/s this time, I've done it a completley different way though. I worked out the height in terms of the volume first then found the derivitive and divided by 600

  6. #6
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    Show the work!

    Hey guys, we will never decide what is correct answer without showing how it was derived.

    Check the following.

    V = Pi*r^2*h/3 (Cone volume in terms of height & radius).

    For cone in question, r = 5*h/8

    Hence V = Pi*(5*h/8)^2*h/3

    or V = 25*Pi*h^3/192

    dV = (25*Pi*h^2/64)*dh

    dV = (25*Pi*16/64)*dh

    dV = (25*Pi/4)*dh

    .1 = (19.635)*dh

    dh = .1/19.635

    dh = .00509 meters/second

    I did not recheck all of the above. If you disagree, show me my error. There might be one.
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  7. #7

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    transcendental analytic kedaman's Avatar
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    I'm sorry there was a typo in the qwestion, the radius should be 10m not the diameter. But that won't affect the methods to solve it, thanks for your input Guv
    Use
    writing software in C++ is like driving rivets into steel beam with a toothpick.
    writing haskell makes your life easier:
    reverse (p (6*9)) where p x|x==0=""|True=chr (48+z): p y where (y,z)=divMod x 13
    To throw away OOP for low level languages is myopia, to keep OOP is hyperopia. To throw away OOP for a high level language is insight.

  8. #8
    Fanatic Member Ianpbaker's Avatar
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    the speed it takes is about the speed it takes arbiter to down a Pint hehehe. sorry just needed to put some humor into this post. back to the assylum I go.
    Yeah, well I'm gonna build my own lunar space lander! With blackjack aaaaannd Hookers! Actually, forget the space lander, and the blackjack. Ahhhh forget the whole thing!

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