   Chapter 1.1, Problem 63E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

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, V=l×b×h.

Area of the rectangle of length l and breadth b is A=l×b.

Calculation:

Since a square of side length x in. is cut out from each corner, the length and the width of the box are l=20xx,w=12xx.

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

V(x)=(202x)×(122x)×x=4x(10x)×(6x)=4x(6016x+x2)=4x364x2+240x

Therefore, the volume of the box as a function of x is V(x)=4x364x2+240x

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