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.

Question

Philoid · Accepted Answer

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.

Write whether True or False and justify your answerThe 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.

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.