Question

An edge of a cube measures 'x'cm .if the largest possible right circular cone is cut out of this cube, then the volume of the cone will be :

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Answer 1

Answer:

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