Find the moment of inertia of a solid hemisphere of mass $M$ and radius $R$ about $A{A}^{\text{'}}$

A disc of radius $R_1$ is cut out from a disc of radius $R_2$ as shown in figure. If the remaining portion of the disc has mass M then find the moment of inertia of the disc left about an axis passing through its centre and perpendicular to its plane.

Moment of inertia of a ring of radius $R$ whose mass per unit length varies with parametric angle $\theta$ according to relation $\lambda ={\lambda }_0{\cos }^2\theta$, about its axis will be

A solid hemisphere $\left(m,R\right)$ has the moment of inertia about axis $1$ (Diameter of hemisphere)

A square plate is of mass $M$ and length of edge equal to $2a$. Its $MI$ about its centre of mass axis, perpendicular to its plane is equal to $I_0$. Four identical disks are cut from the plane. The $MI$ of leftover square about same axis is