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Thread: Error calculation using differential

  1. #1
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    Error calculation using differential

    The circumference of a sphere was measured to be 10 cm with a possible error
    of 0.05 cm. Use differentials to estimate the maximum error in the calculated
    surface area. Thanks!
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    Re: Error calculation using differential

    Hint: \displaystyle \begin{align*} \frac{dA}{dr} \approx \frac{\Delta A}{\Delta r} \implies \Delta A \approx \Delta r \, \frac{dA}{dr} \end{align*}.
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    Re: Error calculation using differential

    I tried to solve it with your hint but still can't.. mind giving me the full solution?
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    Re: Error calculation using differential

    Yes I do mind in fact. The expectation is that students do their own work, and the rules of this site are that if you ask a question, you are supposed to attempt it yourself, show what you have tried (so show all your working out) and exactly where you are stuck. Then we can give you more specific guidance.
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    Re: Error calculation using differential

    (delta)A = dA/dr x (delta)r = 2*Pi*r*0.05 = 10 x 0.05 = 0.5 cm^2
    Is it correct?
    Last edited by yugimutoshung; Jun 8th 2013 at 02:13 AM.
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  6. #6
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    Re: Error calculation using differential

    Is it your radius which has changed by 0.05cm?
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    Re: Error calculation using differential

    So the change in r = 0.05/(2*Pi) ?
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