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Express dV/dt in terms of dr/dt - Derivative Word Problem

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V(t) and its radius is r(t).

    Express dV/dt in terms of dr/dt.


    2. The attempt at a solution

    Volume of a Sphere = 4/3 pi r3

    I took the derivative of the formula above and got: 3pir2_fracdrdt.gif

    I ended up getting: _LARGE__fracdVdt4pir2_fracdrdt.gif

    Did I do this completely wrong? If so, what am I supposed to do?

    Thanks,
    Bob
     

    Attached Files:

  2. jcsd
  3. Oct 13, 2009 #2

    Mark44

    Staff: Mentor

    You're right on the money.

    In LaTeX script, your equation looks like this:
    [tex]\frac{dV}{dt}~=~4\pi r^2 \frac{dr}{dt}[/tex]

    To see the script, click on the expression, and another browser window opens with the LaTeX script.
     
  4. Oct 13, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I don't see anything at all wrong with it!
     
  5. Oct 13, 2009 #4
    Thanks guys!

    Oh, thanks. I've been using a site called Texify to generate all these pictures! This will save a lot of my time in the future.

    Thanks again,
    Bob
     
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