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
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.