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    Minimize the Surface Area of a Box

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    A closed rectangular box with volume 576 in^3 is to be made so its top (and bottom) is a rectangle whose length is twice its width. Find the dimensions of the box that will minimize its surface area.

    Could you please show all work so I can better grasp the concept? Thank you.

    © BrainMass Inc. brainmass.com February 24, 2021, 2:35 pm ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/minimizing-surface-area-box-30576

    Solution Preview

    Suppose this rectangular box has length x, width y and height z.
    From the condition, the length is twice of its width, so x=2y. The volume of the box is ...

    Solution Summary

    The surface area of a box is minimized.

    $2.19

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