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

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Homework Help Overview

The discussion revolves around calculating the percent uncertainty in the area of a circle given a radius of 1.8 x 10^4 cm. Participants are exploring the implications of measurement uncertainty in the context of geometry and uncertainty analysis.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the need for information about the measurement of the radius to determine uncertainty. Some suggest assuming a standard uncertainty based on significant figures, while others express confusion over the calculations and results.

Discussion Status

There is ongoing exploration of the correct approach to calculating percent uncertainty, with some participants providing calculations and others questioning the validity of those results. Multiple interpretations of the uncertainty are being considered, and guidance is being sought for clarity.

Contextual Notes

Participants note the absence of explicit information regarding the uncertainty in the radius measurement, which is crucial for accurate calculations. There is also mention of differing results in percent uncertainty, indicating a lack of consensus on the correct method or interpretation.

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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 [itex]0.1 \times 10^4[/itex] 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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