Let the radius be and error in measuring it be so the measured radius is , then the computed area from the measumenet is:

So the error in the area is and if units and the error is the area is sq-units then:

so:

Alternatively you use , then:

Then if is the maximum permissible error in you solve

Which is equivalent to the earlier method when the terms are ignored. This later method has the advantage that it will still work for more complicated functions (and in particular the function in the next question).

CB