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Calculating % uncertainties

  1. Mar 6, 2016 #1
    A manufacturer needs to determine the volume of metal used to produce a metal pipe of the following dimensions:
    Length, L 40 + 1 m
    External diameter, D 12.0 + 0.2 cm
    Internal diameter, d 10.0 + 0.2 cm
    Estimate the greatest possible percentage error of the volume.

    the correct ans is 22.5%.

    but no matter how many times i've tried, my ans is always 34%. Help pls thank you! :)
  2. jcsd
  3. Mar 6, 2016 #2
    Could you show us your working?
  4. Mar 6, 2016 #3
    V=(pi)(R^2)(L) - (pi)(r^2)(L)


    delta(V) = delta(pi*R^2*L) + delta(pi*r^2*L)

    Let x=(pi)(R^2)(L)

    delta(x)/x = 2(0.1/6) + 1/40= 7/120

    delta(x)=7/120 * (pi*R^2*L)=7/120 * 14 400 pi = 840pi

    Let y=pi*r^2*L

    delta(y)/y = 2(0.1/5) + 1/40=13/200

    delta(y)=13/200 * pi*r^2*L=13/200 * 10 000pi= 650pi

    delta(V) = delta(x) + delta(y)
    delta(V)/V *100% = 1490pi/4400pi *100 = 34%

    fyi 4400pi is the value of V
    thank you
  5. Mar 6, 2016 #4


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    Hi harvey,

    I've moved your thread to the homework forums, but in the future please post all homework questions in the appropriate homework forum and use the template provided.
  6. Mar 6, 2016 #5


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    You have counted the 1/40 twice over. There may be other errors.
    Safest way is just to compute the maximum possible volume.
  7. Mar 6, 2016 #6
    i'm sorry, what do you mean by counting 1/40 twice? is my method not the correct approach anyway?
  8. Mar 6, 2016 #7


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    You counted it here:
    and here:
    Your problem starts with this line:
    Let's back up one step:
    ##\Delta V = \Delta (\pi*R^2*L-\pi*r^2*L)##
    You cannot split that as ##\Delta (\pi*R^2*L)+\Delta(\pi*r^2*L)## because the two terms are not independent.
    If the actual length is L-ΔL on the inner radius it will be L-ΔL on the outer radius. Your analysis exaggerates the range by allowing a volume like
    ##\pi((R-\Delta R)^2(L-\Delta L)-(r+\Delta r)^2(L+\Delta L))##
  9. Mar 7, 2016 #8
    however, it is true that if R=A+B,
    then delta(R) = delta(A) + delta(B).
    i don't get what you mean by independent though. i'm sorry but i just want to fully understand this, thank you!
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