The largest cone that can be cut out of a cube must have its diameter and height equal to the side of the cube. (Refer the diagram)

Thus the dimensions of the cone are:-
diameter = r ; radius = r/2
height = r

We know that volume of a cone = 1/3πr²h
So in this case, volume = 1/3π(r/2)²r
                                    = 1/3πr²/4*r
                                     = 1/12πr³
So that comes  to  1/12πr³ . I guess 1/6πr³ isn't the answer.
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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

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