[Graphs generated by this script: initPicture(-1,10,-5,5);axes(1,1,1,1,1);stroke='blue';strokewidth=2;line([5,3],[8,3]);line([5,-3],[8,-3]);line([8,3],[8,-3]);line([0,0],[5,3]);line([0,0],[5,-3]);]

The graph above shows the base of an object. Compute the exact value of the volume of the object, given that cross sections (perpendicular to the base) are semi-circles, with their diameters on the base.


V=\displaystyle {V}=