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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.8, Problem 15E

(a)

To determine

**To find:** The rate of increase the surface area of the balloon of radius 1 ft.

Expert Solution

The rate of increase of surface area of the balloon of radius 1 ft is,

Surface area of the balloon is,

The rate of change of the balloon with respect to its radius is,

The rate of increase of surface area of radius 1 ft is,

The rate of increase of the surface area of the balloon of radius 1 ft is,

(b)

To determine

**To find:** The rate of increase the surface area of the balloon of radius 2 ft.

Expert Solution

The rate of increase of surface area of the balloon of radius 2 ft is,

Surface area of the balloon is,

The rate of change of the balloon with respect to its radius is,

The rate of increase of surface area of radius 2 ft is,

Therefore, the rate of increase of the surface area of the balloon of radius 2 ft is,

(c)

To determine

**To find:** The rate of increase the surface area of the balloon of radius 3 ft. What can be concluded from the parts (a), (b) and (c)?

Expert Solution

The rate of increase of surface area of the balloon of radius 3 ft is,

Surface area of the balloon is,

The rate of change of the balloon with respect to its radius is,

The rate of increase of surface area of radius 3 ft is,

The rate of increase of the surface area of the balloon of radius 3 ft is,

Thus, the value of the rate of increase of surface area increases as the radius increases.

From the parts (a), (b) and (c), it can be concluded that the rate of change increases as radius increases.