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Homework Help: Volume rate problem

  1. Mar 31, 2008 #1
    1. The problem statement, all variables and given/known data

    The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of chance of the volume when r=6 and r=24 inches.

    2. Relevant equations

    V=(4/3)(pi)(r^3)

    3. The attempt at a solution

    This is what I did, I would appreciate it if someone could tell me if it is correct.

    So the volume of a sphere is V=(4/3)(pi)(r^3)

    So the first thing I did was derive the equation and got this...

    (dv/dt)=(4/3)(3)(pi)(r^2)(dr/dt)

    Simplifying it and plugging in 2 for (dr/dt) i got...

    (dv/dt)=(8)(pi)(r^2)

    So then I just plugged in the r and got 288pi and 4680pi, I have a feeling I've done this terribly wrong though :(
     
  2. jcsd
  3. Mar 31, 2008 #2
    I didn't check your numbers, but your method seems fine to me. However, you might want to get a second opinion before you go and write it in stone.
     
  4. Mar 31, 2008 #3
    It all looks good to me to. Except for when the radius is 24 I got 4608. Maybe you just had a typo there?
     
  5. Mar 31, 2008 #4
    yes sorry that was a typo, thanks! :)
     
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