What you are doing is correct, but you seem to have made some arithmetic errors. Consider:
So but can be in the range
Here is how to reach the same answer using differentials:
So the surface area is , with a relative error of 1.37%
The circumference of a sphere was measured to be cm with a possible error of cm. Use differentials to estimate the maximum error in the calculated surface area.
Estimate the relative error in the calculated surface area.
This is what i tried but i got it wrong?
Circumference of a sphere = 2πr
so r = 11.61831
SA=4πr^2
SA=1696.2731
SAmax=1845.4147
Maximum error = 149.1416 ? this is wrong
Relative error = change in SA / SA
f'sa = 8πr so change in SA = 8π(11.61831)(.5) = 145.9999
relative error = 145.9999/1696.2731 = .08607
can i get some help with what to do because i guess i am doing it wrong
thank you