a. Answer The resulting change in area is 0.08 π Explanation Given information: The radius of a circle is increased from 2.00 to 2.02 m. Calculation: Use differential to estimate the change. d A = A ′ ( a ) d r A = π r 2 A ′ = 2 π r Now substitute the values r = 2 d r = 2.02 − 2 = 0.2 A ′ ( 2 ) = 2 π ( 2 ) = 4 π d A = A ′ ( a ) d r d A = 4 π ( 0.02 ) = 0.08 π Therefore, The resulting change in area is 0.08 π . b. To determine To estimate as a percentage of the circle’s original area. Answer The percentage change in area is 2% of original area. Explanation Given information: The radius of a circle is increased from 2.00 to 2.02 m. Calculation: Divide the estimate change in area by the original area, multiply by 100 to get the estimated percentage change. d A A ( a ) ( 100 ) = 0.08 π π ( 2 ) 2 ( 100 ) = 2 % Therefore The percentage change in area is 2% of original area.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.5, Problem 42E

To determine

To estimate the resulting change in area.

Expert Solution

Answer to Problem 42E

The resulting change in area is 0.08π

Explanation of Solution

Given information:

The radius of a circle is increased from 2.00 to 2.02 m.

Calculation:

Use differential to estimate the change.

dA=A′(a)drA=πr2A′=2πr

Now substitute the values

r=2dr=2.02−2=0.2A′(2)=2π(2) =4πdA=A′(a)drdA=4π(0.02) =0.08π

Therefore,

The resulting change in area is 0.08π .

To determine

To estimate as a percentage of the circle’s original area.

Expert Solution

Answer to Problem 42E

The percentage change in area is 2% of original area.

Explanation of Solution

Given information:

The radius of a circle is increased from 2.00 to 2.02 m.

Calculation:

Divide the estimate change in area by the original area, multiply by 100 to get the estimated percentage change.

dAA(a)(100)=0.08ππ(2)2(100) =2%

Therefore

The percentage change in area is 2% of original area.

Chapter 5.5, Problem 41E

Chapter 5.5, Problem 43E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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