Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Chapter 1, Problem 10P
To determine

The area and its approximate uncertainty of a circle.

Expert Solution & Answer
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Answer to Problem 10P

Solution:

The area of the circle is A=3.0×109cm2

Approximate uncertainty is 6.4% .

Explanation of Solution

Given:

The radius of the circle is 3.1×104cm .

Formula Used:

Area of the circle can be obtained by: A=πr2

Where, r is the radius.

  Percent uncertainty = Absolute uncertaintyAbsolute value ×100 %

Calculation:

Substitute the values:

  A=πr2A=(3.14)(3.1× 10 4cm)2A=3.01754×109cm2

Rounding off to least significant digits: A=3.0×109cm2

  Percent uncertainty =  Absolute uncertaintyAbsolute value ×100 %

From theory of errors:

  A=πr2ln A= ln( πr2)ln A= ln π + 2 ln rΔAA=2ΔrrΔAA=2×0.1× 1043.1× 104ΔAA=0.064Percentage uncertainty  =0.064×100%=6.4%

Conclusion:

The area of the circle is A=3.0×109cm2

Approximate uncertainty is 6.4% .

Chapter 1 Solutions

Physics: Principles with Applications

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