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Math Help - The rate at which the volume of a sphere changes

  1. #1
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    The rate at which the volume of a sphere changes

    Find the rate at which the volume of a sphere is changing with respect to its radius.
    V = (4/3)pi*r

    Any help is appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by lancelot854 View Post
    Find the rate at which the volume of a sphere is changing with respect to its radius.
    V = (4/3)pi*r

    Any help is appreciated. Thanks.
    You need to take the derivative with respect to r

    Note your formula for the volume of a sphere is incorrect

     \displaystyle V=\frac{4}{3} \pi r^3
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  3. #3
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    Oh, I must of written the formula down wrong. xD

    Does this first step look correct?

    \frac{dv}{dx} = \frac{4}{3} \pi 3r^2 \frac{dr}{dx}
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  4. #4
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    Quote Originally Posted by lancelot854 View Post
    Oh, I must of written the formula down wrong. xD

    Does this first step look correct?

    \frac{dv}{dx} = \frac{4}{3} \pi 3r^2 \frac{dr}{dx}
    where did the variable x come from ? the problem statement says to take the derivative w/respect to the radius ...

    \displaystyle \frac{dV}{dr} = 4\pi r^2

    you're done.
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