Find the surface area of a sphere if the area of the lateral surface of a cone inscribed into the sphere with a base

Find the surface area of a sphere if the area of the lateral surface of a cone inscribed into the sphere with a base coinciding with the section of the sphere passing through its center is 6√2

Since the base of the cone coincides with the axial section of the cone, the axial section of the cone, triangle ABC, is rectangular and isosceles, since AC is the diameter of the sphere, and AB and AC are equal as generators of the cone.

Then the ABO triangle is so rectangular and isosceles, and then AB = L = √2 * R see.

The lateral surface area of the sphere is equal to: Sside = π * R * L = π * √2 * R ^ 2 = 6 * √2.

R ^ 2 = 6 / π.

The surface area of the sphere is: Ssf = 4 * π * R ^ 2 = 4 * π * (6 / π) = 24 units2.