Axial section of an isosceles cone, one of the triangles of which is 120 degrees.

Axial section of an isosceles cone, one of the triangles of which is 120 degrees. Find the volume of the cone if its height is 2 ^ 3 cm

The vertex B of the cone is projected to point O, the center of the circle, and is the median and bisector of the isosceles triangle ABC.

Then the angle ABO = 120/2 = 60, and then the angle OAB of the triangle AOB is equal to: OAB = 90 – 60 = 30. The leg OB lies opposite the angle 30, then AB = 2 * OB = 2 * 2 * √3 = 4 * √ 3 cm.

By the Pythagorean theorem, AO ^ 2 = AB ^ 2 – OB ^ 2 = 48 – 12 = 36.

AO = 6 cm.

Determine the volume of the cone.

V = π * AO ^ 2 * ОВ / 3 = π * 36 * 2 * √3 / 3 = π * 24 * √3 cm3.

Answer: The volume of the cone is π * 24 * √3 cm3.