The axial section of the cone is an isosceles triangle ABC.
From the area of the axial section, we determine the length of the base AC of the triangle ABC.
Savs = ОВ * АС / 2.
АС = 2 * Saс / ОВ = 2 * 36/6 = 12 cm.
Then the radius of the circle at the base of the cone is: R = ОА = АС / 2 = 6 cm.
Triangle AOB is rectangular and isosceles, then AB = OA * √2 = 6 * √2 cm.
Let us determine the area of the complete surface of the cone.
Spov = π * ОА * (ОА + AB) = π * 6 * (6 + 6 * √2) = π * 36 * (1 + √2) cm2.
Answer: The surface area of the cone is π * 36 * (1 + √2) 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.