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Math Help - evaporation rate

  1. #1
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    evaporation rate

    this question is giving me a really hard time...

    A spherical drop of radius r(t), r cms, t minutes evaporates at a rate proportional to its surface area. Given that the volume v(t)=4/3╥r^(3) and the surface area s(t)=4╥r^(2), write down an ODE for r(t).

    I am very stuck i have no idea of where to begin, can anyone please help me, Thank you
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  2. #2
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    Quote Originally Posted by acosta0809 View Post
    r cms, t minutes evaporates at a rate proportional to its surface area. Given that the volume v(t)=4/3╥r^(3) and the surface area s(t)=4╥r^(2), write down an ODE for r(t).
    I'll take a punt,

     \frac{dr}{dt} \propto 4\pi r^2 \implies \frac{dr}{dt} =k\times 4\pi r^2

    Now separating

      \frac{dr}{r^2} =k\times 4\pi~dt

    Can you solve this?
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