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Math Help - related rates

  1. #1
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    related rates - still need help!

    A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius of the slick is expanding by 0.1 meter/minute and its thickness is 0.02 meter. At that moment:

    (a) How fast is the area of the slick expanding?
    (b) The circular slick has the same thickness everywhere, and the volume of oil spilled remains fixed. How fast is the thickness of the slick decreasing?

    the answer to (a) is (i hope)
    dA/dt= 2(pi)r (dA/dt)
    dA/dt|r=150 = 30pi

    so for (b).. the area of a cylinder is the area of the top times the height, but i dont know to go from there... do i find dh/dt or somethin? how do i do that?
    Last edited by zintore; July 20th 2008 at 09:23 PM.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by zintore View Post
    A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius of the slick is expanding by 0.1 meter/minute and its thickness is 0.02 meter. At that moment:

    (a) How fast is the area of the slick expanding?
    (b) The circular slick has the same thickness everywhere, and the volume of oil spilled remains fixed. How fast is the thickness of the slick decreasing?

    the answer to (a) is (i hope)
    dA/dt= 2(pi)r (dA/dt) should have been (dr/dt) dA/dt|r=150 = 30pi correct!

    so for (b).. the area of a cylinder is the area of the top times the height, but i dont know to go from there... do i find dh/dt or somethin? how do i do that?
    note that: V_{cyl}=\pi r^2 h and V is contant

    so, \frac{dV}{dt} = \pi r^2 \frac{dh}{dt} + 2\pi r h \frac{dr}{dt}

    can you do from here?
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  3. #3
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    umm

    sorry i still dont understand, how do i find dr/dt?
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  4. #4
    MHF Contributor kalagota's Avatar
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    it was already given:
    the radius of the slick is expanding by 0.1 meter/minute
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  5. #5
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    hmm

    ok now i have dV/dt= 3pi/5 + 450pi dh/dt
    do i answer it in terms of dV/dt like.. (dV/dt -3pi/5)/450pi or... is there a way to solve dV/dt?
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  6. #6
    MHF Contributor kalagota's Avatar
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    it was also given..

    note that
    the volume of oil spilled remains fixed
    that is, the volume is constant.. and what is the derivative of a constant?
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