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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.3, Problem 54E

(a)

To determine

**To express:** The radius of the balloon as a function of time *t*.

Expert Solution

The function of the radius of the balloon in terms of time *t* is

It is given that the balloon is being inflated and therefore the radius is increasing at a rate of 2 cm/s.

Let the radius of the balloon be *r*.

Recall the formula, Distance = Time × Speed.

Note that the distance is same as radius.

Substitute *t* for time and 2 for speed in a distance formula.

Thus, the function is
*r*(*t*) is measured in cm.

Therefore, the radius of the spherical balloon after *t* seconds is

(b)

To determine

**To find:** The expression for
*V* is the volume of the function of radius.

Expert Solution

The value of
*t*.

Area of the circle is,

The composite function

From part (a), the value of

Thus,

Substitute

Thus,
*t*.