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Thread: expanding metal (related rate)

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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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    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.
    $\displaystyle V=\pi r^2h$

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

    $\displaystyle \frac{dh}{dt}=.2$

    $\displaystyle \frac{dr}{dt}=.05$

    $\displaystyle h=400$

    $\displaystyle r=15$
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