Write whether True or False and justify your answer
The volume of the Largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere radius r.
We have
The criteria for the largest cone to fit completely in a cube is that, the vertices of the cone will touch the face of the cube such that the diameter of the cone will be equal to the edge of the cube and height of the cone will be equal to the height of the cube.
Given: edge of cube, l = 2r
Then, diameter of the cone = 2r
⇒ radius of the cone = 2r/2 = r
Height of the cone, h = 2r [that is, height of the cube]
Volume of the cone is given by,
Volume of cone = 1/3 πr2h
= 1/3 πr2(2r) [∵, height of the cone = 2r]
= 2/3 πr3
= Volume of hemisphere of radius r
Hence, it is true.