The height of the cone so formed=the height of the cube i.e.its side.
its diameter=the base side=its other sides.
so the height and diameter of the cone= the side of the cube from which it is cutout.
radius=side by 2,let side be 'r' then:
the vol.of cone=1/3 pi r^2 h,
=1/12 pi r^3
hope this helps