the radius of a circle is measured with an error of measurement which is distributed normal with mean $0$ and variance $\sigma^2$,$\sigma^2$ unknown.Given $n$ independent measurements of the radius , find an unbiased estimator of the area of the circle.
By using Maximum Likelihood Estimator I found
$$\hat\sigma^2=\frac{\sum e_i^2}{n}$$
where $r=r_o+e_i$ is the radius of the circle and $e_i\sim N(0,\sigma^2)$.
Then i am stucked to find the unbiased estimator of the area of the circle