Radial uncertainty scale in a uniform sphere ($r_{\mathrm{rms}}=\sqrt{3/5}R$)

For uniform probability per volume in a sphere of radius $R$, the radial probability density function is $3r^2/R^3$. Its root-mean-square radius is $\sqrt{3/5}R$, whereas its scalar-radius standard deviation is $\sqrt{3/80}R$. These are distinct from a fully specified quantum momentum uncertainty.