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An edge of a cube measures r cm. If the largest possible right circular cone is cut-out of this cube, then prove that the volume of the cone so formed is

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.

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, =1/3*pi*(r/2)^2*r =1/3*pi*r^2/4*r =1/12 pi r^3 hope this helps