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

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.

• compute the cross sectional area with circumference 7 feet 11 inches and 8 feet 1 inch. – Don Thousand Nov 30 '18 at 17:00
• People tend to be more interested here in questions that show an effort to solve the problem, showing in detail what you did and where you got stuck so someone might help you past that specific difficulty. Please see math.stackexchange.com/help/how-to-ask – David K Nov 30 '18 at 17:00
• I have updated the post David – ovil101 Nov 30 '18 at 17:12
• I think error propagation formula would be more efficient and meaningful rather than brute force calculation of limiting cases. – ggcg Nov 30 '18 at 17:29

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=$$r^2$$.

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