# 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 1/6 pi r^3 (in cm^3). Please elucidate! :-)

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by abcxyz

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by abcxyz

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Thus the dimensions of the cone are:-

diameter = r ; radius = r/2

height = r

So in this case, volume = 1/3π(r/2)²r

= 1/3πr²/4*r

= 1/12πr³

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