Answer:
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Explanation:
To find the dimensions of the rectangular box that require the least amount of material for its construction, we can follow these steps:
Determine the volume of the box. The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the box.
Determine the surface area of the box. The surface area of a rectangular box is given by the formula SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the box.
Minimize the surface area while keeping the volume constant. To minimize the surface area, we can try different combinations of l, w, and h and choose the combination that results in the smallest surface area while still maintaining the required volume. This can be done by setting up and solving a system of equations.
Calculate the minimum material required for the construction of the box. Once we have found the dimensions that minimize the surface area, we can use the surface area formula to calculate the minimum amount of material required for the construction of the box.
Construct the box using the minimum amount of material. Once we have calculated the minimum amount of material required, we can use this information to construct the box using the least amount of material possible.