Find the volume of the cone if its diameter is 4 cm, and the generatrix is inclined to the base plane at an angle of 60 degrees.

The axial section of the cone is the isosceles triangle ABC.

The height of the triangle ABC is the height of the cone and the bisector and the median of the triangle ABC.

Then AO = AC / 2 = 4/2 = 2 cm.

Then the ABO triangle is rectangular.

tgBAO = BO / AO.

ВO = AO * tg60 = 2 * √3 cm.

Determine the area of the base of the cone.

Sb = π * R ^ 2 = π * 4 cm2.

Then the volume of the cone is:

V = Sbase * ВO / 3 = π * 4 * 2 * √3 / 3 = π * 8 * √3 / 3 cm3.

Answer: The volume of the cone is π * 8 * √3 / 3 cm3.