A cardboard box without a lid is to be made with a volume of 4 cubic feet. Find the dimensions of the box (in feet) that require the least amount of cardboard. Separate the dimensions with commas, and do not include units in the answer.

(2, 2, 1)

Step-by-step explanation:

A squared based will yield the least amount of cardboard for the box. Thus, the volume of the box is:

Where 'x' is the length of the sides of the base and 'h' is the height of the box.

The total area of cardboard used is:

The value of 'x' for which the derivate of the area function is zero, is the base dimension that will yield the least amount of cardboard:

The height of the box is then:

The dimensions of the box are 2 ft x 2 ft x 1 ft (2, 2, 1).

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step-by-step explanation: