BuyFind

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

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

Answer to Problem 15E

The rate of increase of surface area of the balloon of radius 1 ft is, s(1)=8πft2/ft.

Explanation of Solution

Surface area of the balloon is, s=4πr2.

The rate of change of the balloon with respect to its radius is, s(r)=8πr.

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

s(1)=8π(1)=8πft2/ft.

The rate of increase of the surface area of the balloon of radius 1 ft is, s(1)=8πft2/ft.

(b)

To determine

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

Expert Solution

Answer to Problem 15E

The rate of increase of surface area of the balloon of radius 2 ft is, s(2)=16πft2/ft.

Explanation of Solution

Surface area of the balloon is, s=4πr2.

The rate of change of the balloon with respect to its radius is, s(r)=8πr.

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

s(1)=8π(2)=16πft2/ft.

Therefore, the rate of increase of the surface area of the balloon of radius 2 ft is, s(2)=16πft2/ft.

(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

Answer to Problem 15E

The rate of increase of surface area of the balloon of radius 3 ft is, s(3)=24πft2/ft.

Explanation of Solution

Surface area of the balloon is, s=4πr2.

The rate of change of the balloon with respect to its radius is, s(r)=8πr.

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

s(1)=8π(3)=24πft2/ft.

The rate of increase of the surface area of the balloon of radius 3 ft is, s(3)=24πft2/ft.

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.

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