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Math Help - Related Rates

  1. #1
    lpd
    lpd is offline
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    Related Rates

    Hi. I'm having trouble with this question:

    Oil is spilling from a platform at a constant rate Q and forms a circular spot of constant thickness 10cm. It is observed that when the radius is 100m the radius is changing at a rate of 5 m/hr.

    a) How fast is the area of the spill changing at this instance?
    b) calculate the value of Q.

    My attempt
    a) where

    so m^2/hr

    b) I'm not sure what is Q...
    does it have anything to do with

    where

    therefore, m^2/h

    any help would be great!
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  2. #2
    MHF Contributor

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    The problem said "Oil is spilling from a platform at a constant rate Q" so Q is the rate at which oil is being spilled. It is, specifically, the rate of change of the volume of oil. Since the oil slick is 10 cm high, its volume, in cubic meters, is 0.1A where A is the area. The rate of change is Q= \frac{d(0.1A)}{dt}= 0.1\frac{dA}{dt} and its units are cubic meters per hour.
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