Is it really Geometry?
A right circular cone has a base with radius that is equal to the arithmetic average of the cone's height and generatrix. Given that the volume of the cone is 128π m³, what is the value, in meters, of the base's radius and the height of the cone, respectively?
Note: this problem was not created by me. It is from the Technological Institute of Aeronautics (in Portuguese, Instituto Tecnológico de Aeronáutica, ITA).