Find the moment of inertia of a hemisphere of mass $M$ and radius $R$ shown in the figure, about an axis  AA tangential to the hemisphere.

 

Moment of inertia about an axis through the flat face of hemisphere

$I_G=I_B-m{\left(\frac{3}{8}R\right)}^2=\frac{2}{5}m{R}^2-\frac{9}{64}m{R}^2=\left(\frac{83}{320}\right)m{R}^2$

Using parallel axis theorem, Moment of inertia about the axis  AA',

$I=I_G+m{\left(\frac{5}{8}R\right)}^2 \iff I=\left(\frac{13}{20}\right)m{R}^2$