Answer
$127\space Mgm^{2}$
Work Step by Step
Please see the attached image below.
Here we use the equation $I=\sum m_{i}r_{i}^{2}$ where $I$ - rotational inertia, $m_{i}$ - mass of the i th point & $r_{i}$ - Its distance from the rotation axis. We can write,
$I= Rotational\space inertia\space +\space Rotational\space inertia\space of$
$\space\space\space\space\space\space\space\space\space of\space centrifuge(I_{1})\space\space\space\space\space\space\space \space astronauts\space with \space seats(I_{2})$
Since this is treated as a thin rod, we can write,
$I_{1}=\frac{1}{12}ML^{2}$, Where M - Mass of the centrifuge, L - Length of the centrifuge
$I=\frac{1}{12}ML^{2}+2mR^{2}$; Let's plug known values into this equation.
$I=\frac{1}{12}\times3880\space kg\times(18\space m)^{2}+2\times(105+72.6)kg\times(7.92\space m)^{2}$
$I=104760\space kgm^{2}+22280.4\space kgm^{2}$
$I=127\space Mgm^{2}$
