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Standard errors in surface areas and volumes?

  1. Sep 17, 2010 #1
    I have to finish this one question that I have come across and I am having a bit of trouble figuring out where to go from what I havee done.
    The Q is:

    A copper cylinder is 5.82 +/- 0.06 cm long and has a radius of 2.53 +/- 0.04 cm. Using the appropraite formula,
    Question Details
    a) Find the total surface area of the cylinder and the standard error in the area .
    b) Find the volume of the cylinder and the standard error in the volume.
    c) Given that the density of copper is 8.96cm^-3, find the mass of the cylinder

    We are to use error propogation formulas for this.

    For part a and b I calculated the normals and for b- volume and used the formulae for product rules to calculate the error in volume and found it to be 2.88.

    Can someone guide me through the process because I have the formulas and I plug in the values but I am not sure If i am right or not.

    Thank you.
  2. jcsd
  3. Sep 18, 2010 #2


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    Science Advisor
    Homework Helper

    I prefer to remember just this formula and see how it applies in any particular problem. In this case, for example, the volume of the cilinder would be given by [itex]V = \pi r^2 \ell[/itex] where r is the radius and [itex]\ell[/itex] its length.
    Since both of these have an uncertainty associated to them, you can calculate
    [tex]\frac{\partial V}{\partial \ell} = \pi r^2, \quad \frac{\partial V}{\partial r} = 2 \pi r \ell[/tex]
    and simply plug in your values for [itex]r, \ell, \delta r \text{ and } \delta\ell[/itex].
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