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Math Help - expanding metal (related rate)

  1. #1
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    Post expanding metal (related rate)

    A metal rod is in the shape of a right circular cylinder. As it is heated its length is changing at a rate off 0.2 mm/min and its radius is changing at a rate of 0.05 mm/min. How fast is the volume changing when the rod is 40cm long and 3 cm in diameter?

    This one has me completely lost.
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  2. #2
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    Quote Originally Posted by hotdogking View Post
    A metal rod is in the shape of a right circular cylinder. As it is heated its length is changing at a rate off 0.2 mm/min and its radius is changing at a rate of 0.05 mm/min. How fast is the volume changing when the rod is 40cm long and 3 cm in diameter?

    This one has me completely lost.
    V=\pi r^2h

    \frac{dV}{dt}=\pi(r^2\frac{dh}{dt}+h(2r\frac{dr}{d  t}))

    \frac{dh}{dt}=.2

    \frac{dr}{dt}=.05

    h=400

    r=15
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