The axial section of the cone is an equilateral triangle with an apex angle of 120. The generatrix of the cone is 6cm

The axial section of the cone is an equilateral triangle with an apex angle of 120. The generatrix of the cone is 6cm. find the volume a ball circumscribed about a cone.

Triangle ABC is isosceles with an apex angle B = 120.
The height BO1 of the triangle ABC is also its median and bisector, then the angle ABO1 = 120/2 = 60.
From the point O, the center of the sphere, we construct its radius OA and OB.
In triangle AOB, side OA = OB = R, then triangle AOB is isosceles, and since angle ABO = ABO1 = 60, then triangle AOB is equilateral, OA = OB = R = AB = 6 cm.
Let us determine the volume of a sphere described about a cone. V = 4 * π * R3 / 3 = π * 288 cm3.
Answer: The volume of the ball is π * 288 cm3.