Find the lateral surface of the cone, the axial section of which is an isosceles triangle

Find the lateral surface of the cone, the axial section of which is an isosceles triangle with an apex angle of 120 and a lateral side of 6√3 cm

The axial section of the cone is an isosceles triangle ABC, then the height of the ВO of the cone is the bisector of its apex angle. Then the angle ABO = 120/2 = 600.

In a right-angled triangle AOB SinBAO = AO / AB.

AO = R = AB * SinBAO = 6 * √3 * √3 / 2 = 9 cm.

Let us determine the area of the lateral surface of the cone.

Side = π * R * L = π * AO * AB = π * 6 * 9 * √3 = π * 54 * √3 cm2.

Answer: The area of the lateral surface of the cone is π * 54 * √3 cm2.