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Math Help - Solving problem using derivative

  1. #1
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    Post Solving problem using derivative

    There is a coffee mashin (picture in the attachment )which coffee is falling from the filter to a cylinder with speed of 150 cm^3/min.
    How much is the speed of decreasing the heigh of coffee in the filter when the height is 12.5 cm in the filter?
    Solving problem using derivative-dsc-0000170.jpg

    Thanks for your help.
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  2. #2
    Senior Member BAdhi's Avatar
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    get an equation for the volume of the liquid in the filter with height as the variable.

    differentiate volume with respective to the time. then you'll get an expression with h, \frac{dV}{dt} and \frac{dh}{dt} (h is the height).
    you know h, \frac{dV}{dt}. substitute and find \frac{dh}{dt}.
    Last edited by BAdhi; January 9th 2011 at 04:43 AM.
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by hejmh View Post
    There is a coffee mashin (picture in the attachment )which coffee is falling from the filter to a cylinder with speed of 150 cm^3/min.
    How much is the speed of decreasing the heigh of coffee in the filter when the height is 12.5 cm in the filter?
    Click image for larger version. 

Name:	DSC-0000170.jpg 
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ID:	20367

    Thanks for your help.
    r=\frac{h}{2}

    V=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi (\frac{h}{2})^2h=\frac{1}{12}\pi h^3

    \frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}

    Now just substitute the given values to find \frac{dh}{dt}.
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