Error in cross sectional area of a cylinder, given circumference is $8$ feet $\pm 1$ inch

Question

Given a cylinder with the circumference of $8$ feet $\pm 1$ inch, how could the error in the cross sectional area be found?

As per request:

Given that the area of the cross section is a circle, $A=\pi r^2$, and the circumference is just $C=2 \pi r$. In terms of the area $\pi (C/(2\pi))^2$. I am not sure what to do after that. I know I have to use differentials but I'm not sure how to relate the two.

Answer 1

Use Circumference=$2πr$ given that r is only data to be measured and, $2π$ are both constant.The uncertainty in r (∆r = 1 foot). Now you can easily find uncertainty in Area since Area=$r^2$.

$$Percentage Uncertainty= \frac{2∆r}{r} $$
$$ error=\frac{PU}{100}.Area$$

Now you have the answer.