For the circle:

$r = \var{q(r["A"],units)} \qquad A = \pi r^2 = \var{q(area["A"],units+'^2')}$

$\bar{x} =\var{q(centroid["A"][0],units)} \qquad \bar{y} = \var{q(centroid["A"][1],units)}$

Place a vertical axis through the centroid of the Circle.  The centroidal moment of inertia with respect to this axis is:

$\bar{I}  = \dfrac{\pi r^4}{4} = \var{q(Ibar[axis]["A"],units+'^4')}$

and the distance between the parallel axes is:

$d = \var{q(abs(d[axis]["A"]),units)}$

Applying the parallel axis theorem and the definition of radius of gyration:

$I_{\var{axis}} = \bar{I} + A d^2 = \var{q(I'[axis]["A"],units+'^4')}$

$k_{\var{axis}} = \sqrt{\dfrac{I_{\var{axis}}}{A}} = \var{q(k[axis]["A"],units)}$

For the semi-circle:

$r = \var{q(r["B"],units)} \qquad A = \dfrac{\pi r^2}{2} = \var{q(area["B"],units+'^2')}$

$\bar{x} = \var{latex( offset(0,centers["B"], radii["B"]))} \var{q(centroid["B"][0],units)} \qquad \bar{y} = \var{latex( offset(1,centers["B"], radii["B"]))} \var{q(centroid["B"][1],units)}$

Place a vertical axis through the centroid of the Semi-circle.  The centroidal moment of inertia with respect to this axis is:

$\bar{I}  =\var{ if(orientation=axis,latex("0.1098 r^4"),latex("\\dfrac\{\\pi r^4\}\{8\}")) }= \var{q(Ibar[axis]["B"],units+'^4')}$

and the distance between the parallel axes is:

$d = \var{q(abs(d[axis]["B"]),units)}$

Applying the parallel axis theorem and the definition of radius of gyration:

$I_{\var{axis}} = \bar{I} + A d^2 = \var{q(I'[axis]["B"],units+'^4')}$

$k_{\var{axis}} = \sqrt{\dfrac{I_{\var{axis}}}{A}} = \var{q(k[axis]["B"],units)}$