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Approximate uncertainty in area of circle

  1. Sep 8, 2011 #1
    1. The problem statement, all variables and given/known data
    What is the approximate uncertainty in the area of a circle of radius 5.3 * 104 cm? Express your answer using one significant figure.


    2. Relevant equations
    A = pi*r2


    3. The attempt at a solution
    Using the given radius, I found the area to be 8.8 * 109 cm2.

    And since the uncertainty is not given, I'm assuming that it's 0.1 * 104 cm.

    Using this, the upper limit for the radius is 5.4 * 104 cm, which makes the upper limit for the area 9.2 * 109 cm2.

    Subtracting 9.2 - 8.8 = 0.4 * 109 cm2. But this is apparently not the correct answer, and I can't figure out why. Unless I'm forgetting some fundamental aspect of significant figures, the only other way I can express this in one sig fig is to write out the actual number, i.e. 400000000; but this is also incorrect.

    What am I doing wrong?
     
  2. jcsd
  3. Sep 9, 2011 #2
    If the area is A = pi*r2, then the difference in area is delta-A (sorry, I forgot all my latex). Can you relate delta-A to delta-r (the radius)? If you've taken calculus, then instead of delta-A it would be dA/dr.
     
  4. Sep 9, 2011 #3
    I just figured it out.

    Turns out it was a rounding error on my part, so what I rounded up to 4 * 108 should have actually been rounded down to 3 * 108.
     
  5. Sep 9, 2011 #4

    NascentOxygen

    User Avatar

    Staff: Mentor

    That's the upper bound, now what's the lower bound?
     
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