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Math Help - Need help with related rates

  1. #1
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    Need help with related rates

    Im trying to understand related rates here and im getting stuck at this word problem.

    It says if V is the volume of a sphere with radius r, and the volume of the sphere decreases as the time passes. express dV/dt in terms of dr/dt. Describe the relationship in words.

    I dont get what it means by dV/dt in terms of dr/dt, i know what the derivatives and related rates mean, but I have trouble connecting them to each other.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Sky12 View Post
    Im trying to understand related rates here and im getting stuck at this word problem.

    It says if V is the volume of a sphere with radius r, and the volume of the sphere decreases as the time passes. express dV/dt in terms of dr/dt. Describe the relationship in words.

    I dont get what it means by dV/dt in terms of dr/dt, i know what the derivatives and related rates mean, but I have trouble connecting them to each other.
    Volume of sphere:

    <br />
V=\frac{4}{3}\,\pi\,r^3<br />

    so:

    <br />
\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\,3\,r^2\, \frac{dr}{dt}=4\,\pi\,r^2\, \frac{dr}{dt}

    RonL
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