$2)$ For the plane area shown,

a$)$ Determine the location of the centroid.

b$)$ Calculate the volume of the object that is obtained rotating this area $\backslash (360^\{\backslash$circ$\}\backslash )$ about $\backslash ($ y $\backslash )-$axis.

c$)$ Calculate the volume of the object that is obtained rotating this area $\backslash (180^\{\backslash$circ$\}\backslash )$ about x $-$axis.