# The function that models circumference C of circle in terms of its area A .

### 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 10P
To determine

## To find: The function that models circumference C of circle in terms of its area A .

Expert Solution

The function that models circumference C of circle in terms of its area A is C24π .

### Explanation of Solution

The area of circle is,

A=πr2

Where r is radius of circle.

To model area in terms of circumference, calculate r in terms of C .

Circumference of a circle is,

C=2πrr=C2π

Summarize all the information in a table as shown below.

 In Words In Algebra Area πr2 Circumference 2πr Radius C2π

Use the information in the table and model the function.

A=πr2=π(C2π)2=πC24π2=C24π

Hence, the function that models area of circle in terms of its circumference is C24π .

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