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Math Help - [SOLVED] Speed of increase

  1. #1
    Junior Member Revy's Avatar
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    [SOLVED] Rate of increase

    Could someone help me with this one?

    Sphere radius is increasing in the course of time. At the time moment when it's radius is 8cm, it's increasing in 5cm/s speed. At what speed does spheres volume increase?
    Last edited by Revy; March 1st 2010 at 03:21 PM.
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  2. #2
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    Quote Originally Posted by Revy View Post
    Could someone help me with this one?

    Sphere radius is increasing in the course of time. At the time moment when it's radius is 8cm, it's increasing in 5cm/s speed. At what speed does spheres volume increase?
    \frac{dV}{dt}=\frac{d}{dt}\left(\frac{4}{3}{\pi}r^  3\right)=\frac{4}{3}{\pi}\frac{d}{dt}r^3=\frac{4}{  3}{\pi}\frac{dr}{dt}\frac{d}{dr}r^3

    When r=8, \frac{dr}{dt}=5\ cm/s

    From this, the rate of increase in volume can be calculated.
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  3. #3
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    This is a "relative rates" problem and belongs in "Calculus", not "differential equations".
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  4. #4
    Junior Member Revy's Avatar
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    hm.. is that the same?
    V' = \frac {4}{3}{\pi} {3r^2} {r'} = \frac {4}{3}{\pi}* {3*8^2*5}= 1280{\pi}

    Quote Originally Posted by HallsofIvy View Post
    This is a "relative rates" problem and belongs in "Calculus", not "differential equations".
    Sorry, at first I wasn't sure where I should post it. It's my first time facing english mathematical terms
    Last edited by Revy; March 1st 2010 at 02:38 PM.
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