Moment of Inertia

A uniform square plate $S$ (side $c$ ) and a uniform rectangular plate $R$ (sides $b, a$) have identical areas and masses (Figure).

Show that
$\left(a\right)\frac{I_{xR}}{I_{xS}}<1$
$\left(b\right)\frac{I_{yR}}{I_{yS}}>1$
$\left(c\right)\frac{I_{zR}}{I_{zS}}>1$

Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

With reference to Figure of a cube of edge $a$ and mass $m$, state whether the following are true or false. ($O$ is the centre of the cube).

A uniform square plate has a small piece $Q$ of an irregular shape removed and glued to the Centre of the plate leaving a hole behind (Figure). The moment of inertia about the $z-axis$ is then