Chapter 1.1, Problem 63E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side *x* at each comer and then folding up the sides as in the figure. Express the volume *V* of the box as a function of *x*.

To determine

**To express:** The volume *V* of the box as a function of *x*.

Explanation

**Given:**

Dimension of the rectangular piece of cardboard is 12 in. by 20 in.

Side length of the square is *x* in.

**Formula used:**

Volume of the rectangle of length *l*, breadth *b* and height *h* is,

Area of the rectangle of length *l* and breadth *b* is

**Calculation:**

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

Hence, the volume of the rectangular box is calculated as follows.

Therefore, the volume of the box as a function of *x* is

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