For whatever reason I am incapable of doing this problem.
The circumference of a sphere was measured to be 84 cm with a possible error of .5 cm a) use differentials to estimate the max error in calculated surface area. What is the relative error?
I know that the formula will be $A=4 \pi r^2$ and that the radius is $r= \frac{84}{2\pi}$
know that I will find the error by using differentials where I get
$\frac {dx}{dy} = f \prime (x)$
$ dy = dx f \prime (x)$
$dy=.05 (8\pi r)$ is the same as $dy = .5 (8\pi\frac{84}{2\pi})$
which is the wrong answer. I have no idea what I am doing wrong besides that I suck at math.