Radius of gyration of a body depends on

The moment of inertia of a cylinder of mass $M$,length $L$,and radius $R$ about an axis passing through its centre and perpendicular to the axis of the cylinder is $I = M \left(\frac{R^2}{4} + \frac{L^2}{12}\right)$. If such a cylinder is to be made for a given mass of material,the ratio $L/R$ for it to have the minimum possible $I$ is

Point masses $1, 2, 3$ and $4 \text{ kg}$ are lying at the points $(0,0,0), (2,0,0), (0,3,0)$ and $(-2,-2,0)$ respectively. The moment of inertia of this system about the $x$-axis will be:

The moment of inertia of a solid cylinder of mass $2.5 \ kg$ and radius $10 \ cm$ about its axis is (in $kg \ m^2$)

Three thin rods,each of mass $M$ and length $L$,are placed along the $X$,$Y$,and $Z$ axes,which are mutually perpendicular. One end of each rod is at the origin. The moment of inertia of the system about the $Z$ axis is:

Three bodies have equal masses $m$. Body $A$ is a solid cylinder of radius $R$,body $B$ is a square lamina of side $R$,and body $C$ is a solid sphere of radius $R$. Which body has the smallest moment of inertia about an axis passing through their centre of mass and perpendicular to the plane (in case of lamina)?