The angle of the lateral surface of the cone is 120 degrees, find the diameter of the base of the cone if its generatrix is 15.

The segment OA is the generatrix of the cone, the arc AB is the circumference at its base.

Determine the area of the sector by the formula: Ssec = π * AO2 * α / 360 = π * 225 * 120/360 = 75 * π.

Also Ssec = L * AO / 2, where L is the length of the arc AB.

75 * π = L * 15/2.

L = 75 * 2 * π / 15 = 10 * π cm.

Then L = 2 * π * R = 10 * π.

R = 10/2 = 5 cm.

Then D = 2 * R = 2 * 5 = 10 cm.

Answer: The diameter of the base of the cone is 10 cm.