Question

an edge of a cube measure r if the largest possible right circular cone is cut out of this cube then prove that the volume of the cone in centimetre cube is 1/6πr3

Answer 1

the edge of the cube = r
therefore for cone the largest radius is = r/2
and height of the cone will be = r as all the sides of cube are same 
and formula volume of cone is=1/3 $\pi$$r^{2}$h
when we put values r= r/2
and h=r
therefore 1/3$\pi$$r^{2}$/2*r
=1/6$\pi$r3