uncertainty measurements (and volume)? please help

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mnaceypantsey

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Find the percentage uncertainty of the V of a sphere with r = 19.31 ± 0.13...

I have done this question and done:

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:)
 
mnaceypantsey said:
Find the percentage uncertainty of the V of a sphere with r = 19.31 ± 0.13...

I have done this question and done:

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:)
Click to expand...
When you say your answer is wrong, how do you know that? Also, where does the question come from, and who has the authority to say how you are supposed to solve it? Context can be important (which is why we ask for it).

There are various ways to answer the question, and yours is (almost) one of them. It depends in part on how you define "percentage uncertainty". If this is for a class, what definition has been given?

I say your method is almost right, because as I would define it, the uncertainty is not the range between maximum and minimum, but the deviation of either from the nominal value -- that is, about half of what you said.
 
Dr.Peterson said:
When you say your answer is wrong, how do you know that? Also, where does the question come from, and who has the authority to say how you are supposed to solve it? Context can be important (which is why we ask for it).

There are various ways to answer the question, and yours is (almost) one of them. It depends in part on how you define "percentage uncertainty". If this is for a class, what definition has been given?

I say your method is almost right, because as I would define it, the uncertainty is not the range between maximum and minimum, but the deviation of either from the nominal value -- that is, about half of what you said.
Click to expand...
Sorry for that - I'll clarify!
I know it's wrong because I must input the answer in an automated system, which is giving me "incorrect" for 4.04%. My teacher told me to use calculus... That is the only indication I have been given, unfortunately.

How would I calculate the deviation?
 
mnaceypantsey said:
Sorry for that - I'll clarify!
I know it's wrong because I must input the answer in an automated system, which is giving me "incorrect" for 4.04%. My teacher told me to use calculus... That is the only indication I have been given, unfortunately.

How would I calculate the deviation?
Click to expand...
So, what were you taught about using calculus for this purpose? Surely you were told something specific. Are you learning about differentials, or some other related topic?

If not, I just searched for "percentage uncertainty using derivative" and found this, among others:


That may well not be at quite the right level, but I have no idea what level you need until you tell us something more about your context.
 
in the assignment is written: "% uncertainty is the relative uncertainty as a percentage", and "consider how a change in the radius would affect to a change in the volume".
Unfortunately this is really all the instructions I have...
 
mnaceypantsey said:
in the assignment is written: "% uncertainty is the relative uncertainty as a percentage", and "consider how a change in the radius would affect to a change in the volume".
Unfortunately this is really all the instructions I have...
Click to expand...
No textbook? No current topic you can tell us about that we could use to help you apply it to this problem? Have you tried searching as I did?
 
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