BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 3P
To determine

To find: The function that models volume of a rectangular box with square base in terms of its width whose height is half of width of its base.

Expert Solution

Answer to Problem 3P

The function is modeled as V(w)=12w3 .

Explanation of Solution

Volume (V) of rectangular box with square base is,

Volume=Areaofsquarebase×height

The width of given box is w .

Calculate area of square base.

A=(width)(width)=ww=w2

Model the function in single variable w .

The height (h) of given rectangular box is half of the width of its square base, express it algebraically.

h=w2

Summarize all the information in a table as shown below,

In Words In Algebra
Area of Square base w2
Height of the box w2

Model the function from the information given in the table.

Volume=Areaofsquarebase×heightV(w)=w2(w2)=w32

Thus, the function is modeled as V(w)=12w3 .

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