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The most economical tin can to manufacture is one that is a right circular with height equal to twice the radius. one such can has a volume of 54 pi cm cubed. what is the total surface area of this can in cm squared?

  • algebra -

    Vol =pi(r^2)(2r) = 54pi
    so 2r^3pi = 54pi
    r^3 = 27
    r = 3

    the surface area is made up of 2 circles plus a rectangle with height 2r and length 2pir
    rectangle = 2pi(r)(2r) = 4pi(r^2)
    the 2 cirlces have area of 2pi(r^2)
    so the total area = 6p(r^2)
    = 6pi(9) = 54pi cm^2

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