Uncertainty, volume, and measurement

AI Thread Summary
The discussion revolves around calculating the volume and uncertainty of a sphere with a radius of 19.31 ± 0.13. The user calculated the minimum, average, and maximum volumes but found their percentage uncertainty of 4.04% to be incorrect. They were advised that calculus could help in understanding how to derive uncertainty but were reassured that their current method was acceptable. The conversation highlights the importance of understanding significant figures when reporting uncertainty. Overall, the user seeks clarification on their calculations and guidance on using calculus for better accuracy.
mncyapntsi
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Homework Statement
Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...
Relevant Equations
v=3pi/4r^3
I have done this question and gotten:

Vmin = 4pi/3(19.18)^3=29555.2
V = 4pi/3(19.31)^3=30160.3
Vmax = 4pi/3(19.44)^3=30773.5

Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04% however this is wrong...
Could someone please help me find out where I went wrong, or tell me if I went the wrong direction? I was told I should apparently be using calculus to solve this, but I have no clue where to even start...
Any help would be much much appreciated!

Have a wonderful day
 
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How is the uncertainty defined?
 
mncyapntsi said:
Homework Statement:: Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...
Does this amount to an absolute uncertainty of 0.13 or 0.26?
mncyapntsi said:
Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04%
You may or may not have received guidance about significant figures in reports of uncertainty. It is almost never appropriate to report uncertainty to more than two significant figures.
 
Last edited:
mncyapntsi said:
Homework Statement:: Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...
Relevant Equations:: v=3pi/4r^3

I have done this question and gotten:

Vmin = 4pi/3(19.18)^3=29555.2
V = 4pi/3(19.31)^3=30160.3
Vmax = 4pi/3(19.44)^3=30773.5

Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04% however this is wrong...
Could someone please help me find out where I went wrong, or tell me if I went the wrong direction? I was told I should apparently be using calculus to solve this, but I have no clue where to even start...
Any help would be much much appreciated!

Have a wonderful day
Have you taken calculus yet? Are you familiar with derivatives? Also, why do you think you are wrong?
 
mncyapntsi said:
Homework Statement:: Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...

I should apparently be using calculus to solve this
Note the "plus or minus". How does that compare with your answer of 4%?

You can use calculus. It leads to a useful general result about how small fractional errors in a linear dimension translate into fractional errors in two and three dimensions. But for the purpose of this question, your method is fine.
 
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