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A cardboard box of 32in^3 volume with a square base and open top is to be constructed. What is the length of base that will minimize the surface area?

  • Calculus -


    Surface area = s^2 + 4*s*h

    using volume equation, h=32/s^2

    SA= s^2 + 4*s*(32/s^2) = s^2 + 128/s

    Take derivative dSA/ds and set equal to zero.

    2s - 128/s^2 = 0

    s^3 = 64

    s = 4

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