Question

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! :-)

Answer 1

That proof is not possible, because the volume should come πr³/12 cubic cm, not 1/6.

Volume of original cube = r³ cubic cm.

Cone is of largest size.
Therefore,
=> height of cone = side of cube = r cm
=> diameter of cone = side of cube = r cm
=> radius of cone = diameter/2 = r/2 cm

∴ Volume of cone
= π(radius)²(height)/2
= π(r/2)²*r/3
= πr³/12 cubic cm.

Answer 2

That proof is not possible, because the volume should come πr³/12 cubic cm, not 1/6.

Volume of original cube = r³ cubic cm.

Cone is of largest size.
Therefore,
=> height of cone = side of cube = r cm
=> diameter of cone = side of cube = r cm
=> radius of cone = diameter/2 = r/2 cm

∴ Volume of cone
= π(radius)²(height)/2
= π(r/2)²*r/3
= πr³/12 cubic cm.

Hope it helps you
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