Calculus

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An open top box with a square base is to have a volume of exactly 500 cubic inches. Find the dimensions of the box that can be made with the smallest amount of materials.

  • Calculus -

    your turn to do this one
    I will get you going ...

    base: x by x
    height : y
    V = x^2 y
    500 = x^2 y
    y = 500/x^2

    SA = base + 4 sides
    = x^2 + 4xy
    plug in y from above
    differentiate
    set that equal to zero and solve

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