Calculating Percent Uncertainty of Circle Area w/ Radius 1.8x10^4 cm

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SUMMARY

The discussion focuses on calculating the percent uncertainty of the area of a circle with a radius of 1.8 x 104 cm. The area is computed using the formula A = πr2, resulting in an area of 1,017,876,020 cm2. The uncertainty in the radius is assumed to be ±0.1 x 104 cm, leading to a calculated percent uncertainty of 11%. The participants clarify the importance of understanding the measurement's uncertainty to accurately determine the percent uncertainty in derived quantities.

PREREQUISITES
  • Understanding of the formula for the area of a circle (A = πr2)
  • Knowledge of significant figures and their role in measurement uncertainty
  • Familiarity with the concept of percent uncertainty
  • Basic proficiency in handling scientific notation
NEXT STEPS
  • Study the principles of measurement uncertainty in physics
  • Learn how to apply significant figures in calculations
  • Explore advanced topics in error analysis and propagation
  • Practice calculating percent uncertainty in various geometric contexts
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Students in physics or engineering courses, educators teaching measurement concepts, and anyone interested in understanding uncertainty in scientific calculations.

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Homework Statement


What is the percent uncertainty in the area of a circle whose raduis is 1.8 x 10^4 cm?

Homework Equations


I calculated A=Pi x r^2 = 1017876020
After that, I am lost...

The Attempt at a Solution



Thanks!
 
Last edited:
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The thing is, I don't know what was used to measure the radius. Can I still know what the uncertainty is to calculate the %age?

Thanks!
 
If I'm not given any direct information about the uncertainty in the initial measurement (here, the radius), I take it to be +/- 1 in the last significant figure. In this case the uncertainty in the radius would be 0.1 \times 10^4 cm.
 
Thanks a lot!

I calculated the percent uncertainty to be 5.6%. I think it is correct...
 
Apparently this is not the correct answer! please help me ...

Thanks!
 
Ok it was 11%... I don't understand why though... If you could walk me through the thinking process, I'd be grateful. I will know how to do such a problem next time... Thanks!
 

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