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: 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?


    Attached Files:

  2. jcsd
  3. Oct 13, 2009 #2


    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


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