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Math Help - Another Cone problem!

  1. #1
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    Another Cone problem!

    Sand is dropping on a pile that is shaped like a cone with the normal volume for a cone. The radius is growing at a rate of 2 cm per minute. The height is growing at a rate of 1cm per minute. How fast is the volume changing when the radius is 10 cm.

    What do you take the derivative of? Before I was trying to take the derivative of the volume and having r be a function of t and h also a function of t... if you could show me the steps it would be a great help!

    Thanks!

    George
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  2. #2
    Eater of Worlds
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    Product rule:

    \frac{dV}{dt}=\frac{\pi}{3}\left(r^{2}\cdot \frac{dh}{dt}+h\cdot 2r\frac{dr}{dt}\right)
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  3. #3
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    h???

    I even got that far, but what do I substitute for h? h was not given, but only the change in h...

    Thanks!
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  4. #4
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    Quote Originally Posted by auswien1180 View Post
    I even got that far, but what do I substitute for h? h was not given, but only the change in h...

    Thanks!
    If the radius is growing at the rate of 2cm per minute,
    then it will have taken x minutes to grow to 10cm.

    Use that value of x to determine h, which grows at 1cm per minute.
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