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Calculating uncertainty when subbing in to a formula? watch

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    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%?
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    I think that the percentage uncertainty should be 10%. Who says that it is 5%? Is this a past paper we can look at?
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    (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
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    (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 . . .

    



r = \sqrt{\dfrac{V}{\pi h}}

    . . . or alternatively . . .

    



r = \bigg(\dfrac{V}{\pi h}\bigg)^{\frac{1}{2}}

    This implies that the percentage uncertainty,  p(\Delta r) , of the radius can be calculated by . . .

    



p(\Delta r) = \frac{1}{2}[p(\Delta V) + p(\Delta h)]

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

    



p(\Delta r) =  \frac{1}{2}[(7\%) + (3\%)]

    



p(\Delta r) =  5\%

    . . .  r has a percentage uncertainty of  5\% .

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

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

    



r = \sqrt{\dfrac{V}{\pi h}}

    . . . or alternatively . . .

    



r = \bigg(\dfrac{V}{\pi h}\bigg)^{\frac{1}{2}}

    This implies that the percentage uncertainty,  p(\Delta r) , of the radius can be calculated by . . .

    



p(\Delta r) = \frac{1}{2}[p(\Delta V) + p(\Delta h)]

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

    



p(\Delta r) =  \frac{1}{2}[(7\%) + (3\%)]

    



p(\Delta r) =  5\%

    . . .  r has a percentage uncertainty of  5\% .

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