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.
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