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Chain rule

  1. Oct 25, 2007 #1
    A cubical block of ice is melting in such a way that each edge decreses steadily by 8.8 cm every hour. At what rate is its volume decreasing when each edge is 5 meters long?

    this is my work

    Let l=l(t) be the length of each edge at time t

    then volume = l^3
    dl/dt = 8.8cm/h = .088m/h

    dV/dt = dV/dl * dl/dt
    = 3l^2 * .088 m/h

    at l = 5
    dV/dt = -6.6m/h

    where have I made an error?

    thanks
     
  2. jcsd
  3. Oct 25, 2007 #2

    Dick

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    I don't see any problem except the units. volume/time isn't m/h.
     
  4. Oct 25, 2007 #3

    HallsofIvy

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    Early on you should have dl/dt= -0.088 m/h but you appear to have put the negative in the final answer. Dick is correct: You need to keep better track of your units. 3 (5 m)2= 75 m2. Multiplying that by -0.088 m/h gives -6.6 m3/h which is correct, of course for rate of change of volume since volume is measured in m3 so the rate of change of volume per hour is m3/h.
     
  5. Oct 25, 2007 #4
    sorry i put in -6.6m^3/h
    thats just a typo

    i'm still getting the wrong answer?
     
  6. Oct 25, 2007 #5

    Dick

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    Why do you think the answer is wrong?
     
  7. Oct 25, 2007 #6
    inputting it for an assignment online and getting an "incorrect" response
     
  8. Oct 25, 2007 #7

    Dick

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    I can't see where it's incorrect. Except for technicalities. They ask for the rate at which it is decreasing. So you would be technically correct to put in a positive number. This 'online' things can be complete idiots.
     
  9. Oct 25, 2007 #8

    cristo

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    Have you checked the units the online thing wants the answer in?
     
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