# Approximate uncertainty in area of circle

1. Sep 8, 2011

### chops369

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. Sep 9, 2011

### daveb

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.

3. Sep 9, 2011

### chops369

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.

4. Sep 9, 2011

### Staff: Mentor

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