1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    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....
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted