From a rectangular piece of cardboard having dimensions a × b, where a = 20 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). express the volume v of the box as a function of x.

The volume of the box as a function of x will be 1400x - 180x² - 4x³.

First and foremost, you should note that the volume of a rectangular prism is given as:

= Length × Width × Height

where,

Length = 70 - 2x

Width = 20 - 2x

Height = x

Volume = Length × Width × Height

Volume = (x)(20 - 2x)(70 - 2x)

Volume = 1400x - 40x² - 140x² + 4x³

Volume = 1400x - 180x² - 4x³

Therefore, the volume of the box as a function of x will be 1400x - 180x² - 4x³.

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