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Rate of Change Problem

  1. Sep 2, 2008 #1
    hi everyone,
    i am having trouble with this rate of change question.
    I need to find the rate of change of a sphere with a volume of V= 4/3*pi*r^3 in respect to it's surface area of A= 4*pi*r^2
    can anyone give me a hand?
  2. jcsd
  3. Sep 2, 2008 #2
    Since the surface area- the derivative of the volume-is A=4*pi*r^2, it would seem that change there would be the derivative, 8*pi*r.
  4. Sep 3, 2008 #3


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    So you want to find dV/dA? Use the chain rule dV/dr= (dV/dA)(dA/dr) so dV/dA= (dV/dr)/(dA/dr). Find dV/dr and dA/dr and divide.
  5. Sep 3, 2008 #4
    so if dV/dr = 4*pi*r^2
    and if dA/dr = 8*pi*r

    i just divide the two?
  6. Sep 3, 2008 #5
    dv/dr = 4/3*pi*3*r^2 = 4*pi*r^2

    da/dr = 4*pi*2*r = 8*pi*r

    dv/da = dv/dr * dr/da = r/2
  7. Sep 3, 2008 #6


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    Well, that is what I said in the post you quoted!

    Lizzie, when a person asks for help, please do not just do the problem for them!
  8. Sep 5, 2008 #7
    ok sorry hallsofivy
  9. Sep 18, 2008 #8
    to find the rate of change for designing of catalytic oxidation converter
    SO2+0.5O2 <---->SO3
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