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DA/dt of expanding circle

  1. Oct 24, 2009 #1
    1. The problem statement, all variables and given/known data
    a) if A is the area of circle with radius r and the circle expands as time passes, find dV/dt in terms of dr/dt
    b)Suppose oil spills from a ruptured ranker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 30 m?


    2. Relevant equations

    A=(pi)r2

    3. The attempt at a solution

    dA/dt= ((pi)r2)'=(r2+2(pi)r)

    dA/dt= ((pi)2(30) + 302)

    is this correct? it seems like an awfully big number what have I done wrong?
     
  2. jcsd
  3. Oct 24, 2009 #2
    oh wait I am treating pi like a variable not a constant. durh
     
  4. Oct 24, 2009 #3
    so dA/dt = 2*30*pi
     
  5. Oct 24, 2009 #4

    Dick

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    You've got it dA/dt=pi*2*r*dr/dt.
     
  6. Oct 24, 2009 #5
    OK so I would need to have multiplied 2*pi*r*1m/s but since its one it doesn't matter but that is what is happening correct?

    I am multiplying the derivative of the expression by the derivative of r?
     
  7. Oct 24, 2009 #6

    Dick

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    It matters if you are keeping track of units. That's where the m/s came from.
     
  8. Oct 24, 2009 #7

    Dick

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    You are using the chain rule. d/dt(f(r))=d/dr(f(r))*dr/dt. You knew that, right?
     
  9. Oct 24, 2009 #8
    I know that now. I missed a good couple classes (long story short) because I had no other choice. Now I am trying to catchup. I guess I better do some reading..thanks
     
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