Approximate uncertainty in area of circle

[chops369]

Homework Statement

What is the approximate uncertainty in the area of a circle of radius 5.3 * 10⁴ cm? Express your answer using one significant figure.

Homework Equations

A = pi*r²

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?

 

[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.

 

[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.

 

[NascentOxygen]

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.

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