The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm

Question

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is :\

Professor PC Thomas Classes · Answer

(d): For largest right circular cone to be carved out, the diameter and the height of the cone must be same as the length of the side of cube.\ i.e., Height of cone $(h)=2 \mathrm{~cm}$\ Diameter of cone $(d)=2 \mathrm{~cm}$\ ⇒ Radius of cone $(r)=1 \mathrm{~cm}$\ ∴ Volume of largest cone $=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \pi 	imes(1)^{2} 	imes 2$ 
$ =\frac{2}{3} \pi \mathrm{cu} \cdot \mathrm{~cm} $