Propagating error for a circle

Question

The radius of a circle is measured to be $12.1\pm 0.030$ cm

What is the uncertainty in the area of this circle?

Thank you for your help!

Answer 1

Three hints, depending on whether you like playing with numbers, algebra, or calculus:

1. Numbers: Calculate the areas of circles with radii 12.1, 12.13, 12.07.

2. Algebra: Expand $\pi(r+\varepsilon)^2$ and see how it differs from $\pi r^2$.

3. Calculus: Ponder $\delta A \approx \tfrac{dA}{dr} \delta r$