Question

The largest right circular cone is cut from out of cube of edge r .what is the volume of cone

Answer 1

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

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