# The function that models the surface area of the balloon as a function of time t .

### 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 2.6, Problem 63E
To determine

## To find: The function that models the surface area of the balloon as a function of time t.

Expert Solution

The function that models the surface area of the balloon as a function of time t is A(t)=16πt2.

### Explanation of Solution

Given:

The radius of the balloon is increasing at the rate of 2cm/s.

Calculation:

Since the radius of the spherical balloon is increasing at the rate of 2cm/s, therefore the relation between radius and time is given as, r=2t (1)

The surface area of the sphere with radius r is , A=4πr2.

Substitute r=2t in A=4πr2 to find the surface area as follows,

A(t)=4π(2t)2=4π(4t2)=16πt2

Thus, the function that models the surface area of the balloon as a function of time t is A(t)=16πt2.

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