# Circumference of Circle with Uncertainty

## Homework Statement

Calculate the circumference (including uncertainty) of a circle whose measured radius is r=7.3 ± 0.2cm.

2.Relevant equations & 3.The attempt at a solution

- Circumference of circle --> C = 2πr = 2π7.3 = 45.87 cm

- Exact constant error propagation --> z = kx

- Limit Error --> δz = kδx

- Therefore, δC = 2π(0.2 cm) = 1.257 cm

Final Answer = 46 ± 1 cm

OR Should I be going about it like this:

- Circumference of circle --> C = 2πr = 2π7.5 = 47.124 cm = 47 cm

- Circumference of a circle --> C = 2πr = 2π7.1 = 44.611 cm = 45 cm

- Final Answer 46 ± 1 cm

I was discussing this with someone else. I did it the first way and they did it the second way.

Also, my final answer has the correct significant figures right?

kuruman
Homework Helper
Gold Member
You should do it the first way. Bracketing the calculated value with the minimum and maximum values using the given uncertainty is for people who are not conversant with calculus and do not understand where ΔC = 2πr Δr comes from. Yes, your final answer has the correct sig. figs.

You should do it the first way. Bracketing the calculated value with the minimum and maximum values using the given uncertainty is for people who are not conversant with calculus and do not understand where ΔC = 2πr Δr comes from. Yes, your final answer has the correct sig. figs.
Thank you! That's what I thought as well :)

Orodruin
Staff Emeritus