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You are planning to make an open-top box from an 12 in by 12 in piece of cardboard
by cutting congruent squares from the corners and folding up the sides.

What are the dimensions (of the 3 sides) of the largest volume you can make this way?

  • calculus -

    let the size of the cut out squares be x by x inches
    so the base of the box is 12-2x by 12-2x and its height is x inches.
    volume = x(12-2x^2

    expand, then find d(volume)dx
    set that equal to zero and solve for x,
    from which you can then find the dimensions

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