# The axial section of the cone is an isosceles triangle with a base of 12 cm and an apex angle

The axial section of the cone is an isosceles triangle with a base of 12 cm and an apex angle of 60 degrees. Find the surface area of a cone.

The axial section of the cone is an isosceles triangle ABC, the base of which is the diameter of the circle at the base of the cone, AC = 12 cm.

Then the radius of the circle at the base of the cone is R = AC / 2 = 12/2 = 6 cm.

Since, according to the condition, the angle at the vertex B is equal to 600, then the triangle ABC is equilateral, which means that the generatrix of the cone L = AB = BC = 2 * R = 12 cm.

Determine the surface area of the cone.

Spov = π * R * (R + L) = π * 6 * (6 + 12) = 108 * π cm2.

Answer: The surface area of the cone is 108 * π cm2

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