## Related questions with answers

Solve the given problem.

A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting two-inch squares from each corner and folding up the sides. Let $x$ represent the width of the original piece of cardboard.

(a) Represent the length of the original piece of cardboard in terms of $x$.

(b) What will be the dimensions of the bottom rectangular base of the box? Give the restrictions on $x$.

(c) Determine a function $V$ that represents the volume of the box in terms of $x$.

(d) For what dimensions of the bottom of the box will the volume be $320$ cubic inches? Determine analytically and support graphically.

(e) Determine graphically (to the nearest tenth of an inch) the values of $x$ if the box is to have a volume between $400$ and $500$ cubic inches.

Solution

Verified$a.)$ Since, a piece of a cardboard is twice as long as it is wide and $x$ represents the wide therefore we can say that the length of the original piece of the cardboard in terms of $x$ is $2x$.

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