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Math Help - word problem

  1. #1
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    word problem

    The radius r of a right circular cone is increasing at a rate of 2 inches per minute. The height h of the cone is related to the radius by h=3r. Find the rates of change of the volume when :

    r = 6 inches
    and
    r = 24 inches

    How can I set up the derivative and solve down? (step by step instruction works best for me )
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by jimmyp View Post
    The radius r of a right circular cone is increasing at a rate of 2 inches per minute. The height h of the cone is related to the radius by h=3r. Find the rates of change of the volume when :

    r = 6 inches
    and
    r = 24 inches

    How can I set up the derivative and solve down? (step by step instruction works best for me )
    V=\frac{1}{3}\pi r^2 h

    Taking the derviative with respect to time gives

    \frac{dV}{dt}=\frac{\pi}{3}\left(2rh \frac{dr}{dt}+r^2\frac{dh}{dt} \right)

    From above we know that h=3r \implies \frac{dh}{dt}=3\frac{dr}{dt}

    From here just plug everything in.

    Good luck
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