# A function that represents the amount of air required to inflate the balloon from a radius of r inches to r + 1 inches . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.1, Problem 24E
To determine

## To find: A function that represents the amount of air required to inflate the balloon from a radius of r inches to r+1 inches .

Expert Solution

The required function is, f(r)=4π(r2+r+13)

### Explanation of Solution

Given information:

The given volume of spherical balloon is,

V(r)=43πr3

Here, r is the radius of the spherical balloon.

The radius of required to inflate the balloon is r+1inches

Concept used:

To represent the function:

A function f is a rule that assigns to each element x in a set D exactly one element called f(x) in a set E

The function f(r) oftheamountofairrequiredtoinflatetheballoonfromaradiusof rinches toa radius of r+1inches is calculated as,

f(r)=V(r+1)V(r)

The given volume of spherical balloon is

V(r)=43πr3

Then,

f(r)=43π(r+1)343π(r)3=43π((r+1)3(r)3)=43π(3r2+3r+1)=4π(r2+r+13)

Therefore, the required function is f(r)=4π(r2+r+13) .

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