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# Calculating uncertainty when subbing in to a formula? watch

1. The volume V of a cylinder of height h and radius r is given by the expression V = πr2h.
In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are :V ±7%, h ± 3%.
Why this is 5% not 10%?
2. I think that the percentage uncertainty should be 10%. Who says that it is 5%? Is this a past paper we can look at?
3. (Original post by Pangol)
I think that the percentage uncertainty should be 10%. Who says that it is 5%? Is this a past paper we can look at?
Maybe so. It's from some online revision notes on the 7th page, it gives the answer below.

http://mrsmithsphysics.weebly.com/up...ties_notes.pdf
4. (Original post by Louiskn)
The volume V of a cylinder of height h and radius r is given by the expression V = πr2h.
In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are :V ±7%, h ± 3%.
Why this is 5% not 10%?
Hello there,

If we rearrange the equation, we find that . . .

. . . or alternatively . . .

This implies that the percentage uncertainty, , of the radius can be calculated by . . .

. . . since the percentage uncertainty within the parentheses is multiplied by the exponent. Therefore . . .

. . . has a percentage uncertainty of .

I hope that this has been helpful.
5. (Original post by Smithenator5000)
Hello there,

If we rearrange the equation, we find that . . .

. . . or alternatively . . .

This implies that the percentage uncertainty, , of the radius can be calculated by . . .

. . . since the percentage uncertainty within the parentheses is multiplied by the exponent. Therefore . . .

. . . has a percentage uncertainty of .

I hope that this has been helpful.
Perfect! Thanks!
6. Ah - the lack of formatting in the question made me look right through the square (I thought it was just a 2). Nice explanation!
7. (Original post by Louiskn)
Perfect! Thanks!
You're very welcome.
8. (Original post by Pangol)
Ah - the lack of formatting in the question made me look right through the square (I thought it was just a 2). Nice explanation!
Thank you,

Yes, indeed- if the equation was as it was written in the question post, then you would have been correct.

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