A right cone, is a solid of revolution generated by the rotation of a right triangle, around one leg. The circle described by the other leg is called the base of the cone and the upper end of the leg, around which is rotated, is called the vertex.
The volume of the cone is equal to one third of the volume of a cylinder that shares the same axis. So, the volume of a cone can be calculated by the following equation:
V = (πr^2h)/3
r, is the radius of the cone base.
h, is the height (distance from the vertex to the center of the base).
Since the volume of our cone is 6π, we can write:
6π = (πr^2h)/3
Solving this equation for the radius, we have:
r^2 = 18/h = 9
r = sqrt (9) = 3 cm
Then, the diameter will be:
d = 2r = 6 cm