# 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. ### Precalculus: Mathematics for Calcu...

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

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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