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Math Help - Differentiation Applications Problem

  1. #1
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    Differentiation Applications Problem

    A solid right circular cylinder has a hemisphere hollowed out from each end. Given that the total surface area is 64pi cm sq, find the radius of the cylinder when the volume is maximum.
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  2. #2
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    Quote Originally Posted by puggie View Post
    A solid right circular cylinder has a hemisphere hollowed out from each end. Given that the total surface area is 64pi cm sq, find the radius of the cylinder when the volume is maximum.
    Surface area
    2\pi r^2+2\pi rh-6\pi r^2=64\pi simplifies to ..

    h=\frac{32+2r^2}{r}

    Volume ..

    V=\pi r^2h-\frac{4}{3}\pi r^3

    Substitute h into this equation . After that , calculate \frac{dV}{dr} then have it equals to 0 to find r .
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