The height of the cone is 4√3 cm, and the angle at the apex of the axial section is 1200.

The height of the cone is 4√3 cm, and the angle at the apex of the axial section is 1200. Find the area of the base of the cone.

The axial section of the pyramid is an isosceles triangle ABC in which the lateral sides are generatrices of the cone, and the base of the AC is the diameter of the circle at its base.

OB is the height of the cone and the height of the triangle ABC, and since it is isosceles, it is also its bisector and median. Then the angle OBC = ABC / 2 = 120/2 = 60, OC = AC / 2 = R.

Through the tangent of the OBC angle, we determine the length of the OS radius.

tg60 = OC / OB.

OS = R = OB * tg60 = 4 * √3 * √3 = 12 cm.

Then Sop = π * R2 = 144 * π cm2.

Answer: The area of the base of the cone is 144 * π cm2.