# A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in. by 22 in. by cutting out equal squares of side x at each corner and then folding up the sides . Express the volume V of the box as a function of x.

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A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in. by 22 in. by cutting out equal squares of side x at each corner and then folding up the sides . Express the volume V of the box as a function of x.

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Step 1

Given,

The dimension of the rectangular piece of cardboard is 14 in. by 22 in

And we construct a box with an open top by cutting out equal squares of side x at each corner and then folding up the sides.

Step 2

Let the side length of the square is x in.

Since a square of side length x in is cut out from each corner, the length and width of the box are

Step 3

Therefore, the volume of th...

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