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5. What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of .8L?


    That depends upon how thick you make the walls of the cone. They should have asked for the minimum surface area cone with that volume.

    The surface area of a cone is:

    A = pi s r
    = pi*sqrt(r^2 + h^2)*r
    where s is the slant height and h is the height of the axis.

    The cone volume must satisfy (1/3)pi*r^2*h = 800 cm^3, so
    h = 2400/(pi*r^2)

    Write A as a function of r only and differentiate A(r). Set the derivative equal to zero and solve for r.

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