Calculating Percent Uncertainty in Area of a Circle

[fattydq]

I am asked "What is the area and it's approximate uncertainty of a circle of radius 3.8x10^4 cm?"

Now finding the area is easy. In my text it says that when you aren't GIVEN an uncertainty, you can assume it is a reasonable figure in the last digit, so in this problem I am assuming the original value is 32,000 cm +/- 5 cm. So far so good...

Now, how do I find the percent uncertainty of my final answer? Because I know the percent uncertainty in my 32,000 cm figure, but how does this come into play after squaring it and multiplying it by pi?

 

[tiny-tim]

Welcome to PF!

I am asked "What is the area and it's approximate uncertainty of a circle of radius 3.8x10^4 cm?"

Hi fattydq! Welcome to PF!

Surely the "last digit" is the 8 … the question says 3.8x10⁴ cm, not 3.8000x10⁴ cm ?

If you have an error of 1% in something, does the error change if you multiply that something by π?

And what happens if you square it (try it, and see)?

 

[fattydq]

I thought if you had a percent uncertainty...and multiplied it by something else with percent uncertainty, that you would add the two values to get the final percent uncertainty?

 

[tiny-tim]

That's right!

So if you square something, then the uncertainty … ?