Answer
See answer.
Work Step by Step
Let’s first calculate the area, using the specified radius.
$A_{middle} = \pi r_{middle}^2=\pi(3.1\times10^4 cm)^2=3.019\times10^9 cm^2$
Next, find the area using the minimum radius, then using the maximum radius. The uncertainty in the radius is assumed to be $0.1 \times 10^4 cm$.
$A_{min} = \pi r_{min}^2=\pi(3.0\times10^4 cm)^2=2.827\times10^9 cm^2$
$A_{max} = \pi r_{max}^2=\pi(3.2\times10^4 cm)^2=3.217\times10^9 cm^2$
The uncertainty in the area is approximately half of this range.
$\Delta A=\frac{1}{2}(A_{max}-A_{min})=0.195\times10^9 cm^2$
Quote the area as $ (3.0 \pm 0.2)\times10^9 cm^2$.
