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Related RateArea of Circle

  1. Jan 3, 2012 #1
    1. The problem statement, all variables and given/known data
    A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. Does the area also increase at a constant rate?


    2. Relevant equations
    A = ∏r2

    3. The attempt at a solution
    dA/dt = 2∏r(dr/dt)
    dA/dt = 2∏r(3ft/s)

    What now?
     
  2. jcsd
  3. Jan 3, 2012 #2

    Mark44

    Staff: Mentor

    Now you answer the question - Is the area increasing at a constant rate?
     
  4. Jan 3, 2012 #3
    I mean, I guess it would, but I don't really know how to explain it.
     
  5. Jan 3, 2012 #4

    Mark44

    Staff: Mentor

    The radius is increasing at a constant rate, since dr/dt = 3 (ft/sec).

    The rate of change of the area is dA/dt = 6[itex]\pi[/itex]r (ft2/sec). Does that look like a constant to you?
     
  6. Jan 3, 2012 #5
    Yes.
     
  7. Jan 3, 2012 #6

    Mark44

    Staff: Mentor

    A constant value shouldn't have a variable in it. The value of dA/dt depends on how big the circle is - IOW, dA/dt is NOT constant.
     
  8. Jan 3, 2012 #7
    Ok thanks I was very confused on this but you helped.
     
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