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Math Help - related rates

  1. #1
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    related rates

    oil from a leaking oil tanker radiates outward in the form of a circular film on the surface of the water. If the radius of the circle increases at the rate of 3 meters per min, how fast is the area of the circle increasing when the radius is 200 meters ?

    π x r^2= area of circle

    therefore
    π x200^2=125663.71

    125663.71x3 = 376991.12

    according to the book the answear is wrong as they have 1200
    π m^2/min

    they did not show any working !

    also

    differencite this

    F(x) = √ (x-1)/(x+1)

    an simplify!

    cheers !
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  2. #2
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    Re: related rates

    Quote Originally Posted by arsenal12345 View Post
    oil from a leaking oil tanker radiates outward in the form of a circular film on the surface of the water. If the radius of the circle increases at the rate of 3 meters per min, how fast is the area of the circle increasing when the radius is 200 meters ?

    π x r^2= area of circle

    therefore π x200^2=125663.71

    125663.71x3 = 376991.12 ... this is incorrect

    according to the book the answear is wrong as they have 1200π m^2/min
    A = \pi r^2

    take the derivative of the above equation w/r to time ...

    \frac{dA}{dt} = 2\pi r \cdot \frac{dr}{dt}

    sub in your givens ... you'll get the answer the text provides.
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  3. #3
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: related rates

    A=area
    r=radius
    t=time

    A(t)=Pi*r(t)^2
    dA/dt=2*Pi*r*dr/dt

    at r=200, dr/dt=3 we obtain rate of increase of area as:
    2\pi (200)3 = 1200 \pi sq m/min
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  4. #4
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    Re: related rates

    thanks buddy , any luck with the second question?
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  5. #5
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: related rates

    dF/dx=\frac{1}{\sqrt{x-1} (x+1)^{3/2}}
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  6. #6
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    Re: related rates

    Quote Originally Posted by arsenal12345 View Post
    thanks buddy , any luck with the second question?
    depends ... which is the function you posed?


    \frac{\sqrt{x-1}}{x+1}

    or

    \sqrt{\frac{x-1}{x+1}}
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