The area of the axial section of the cone is 36 cm2, the height is 6.find the total surface area of the cone

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.