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Calculus Rates Question?

  1. Apr 17, 2013 #1
    1. The problem statement, all variables and given/known data
    A rectangular object has a fixed length of 1m. The height is increasing by 12 cm/min. Find the rate that the width must change so that the volume remains constant at 16 000cm^3 when the height is 10 cm





    3. The attempt at a solution

    So heres what I tried:

    The Volume= Lenth x Width x Height
    V = x y z Since x is fixed at 100 , V= 100 y z
    dV/dt = 100y dz/dt +100 z dy/dt = 0
    z dy/dt = -ydz/dt
    (10) (12) = - y dz/dt
    When x= 100 and z= 10 and V=16000 , y = 16
    dz/dt = - (10)(12)/y = - 120/16 = -7.5 cm/min


    However, I dont even know if I am taking the right approach... Please give me assistance
     
  2. jcsd
  3. Apr 17, 2013 #2

    Mark44

    Staff: Mentor

    Looks OK to me, but I didn't check that closely. It's reasonable to get a negative rate, since one dimension is increasing, and one is constant. It has to be true that the third dimension is decreasing, this you get a negative rate.

    It would have been helpful to use variables that matched what they represent - h for height, and w for width. I have to do a bit of translation with y and z.
     
  4. Apr 17, 2013 #3
    Ok sorry about the representation thing but is my approach correct? I just dont understand why I didnt have to use the chain rule....
     
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