A right circular cone has a base radius of $6$ cm and a height of $8$ cm. A cube-shaped box is inside the cone so that one face of the box is contained in the base of the cone and the four upper corners are in contact with the inner curved surface of the cone.
Furthermore, there is a spherical ball that rests on top of the box,touching the inner curved surface of the cone.
Find the ratio of the volume of the ball to that of the box.
I tried to find the length of the edge of the box.But i could not figure it out as it is $D$.