(Originais Teachy 2024) - Question Medium of Mathematics

Consider a right cone whose generatrix measures 10 cm and whose lateral surface is cut in such a way that, when opened and arranged on a plane, it forms a circular sector with a central angle of 60 degrees. Knowing that the line connecting the vertex of the cone to the midpoint of the base is perpendicular to the base plane and that the base radius measures 6 cm, determine: (1) The measure of the radius of the cone's cross-section formed by the cut. (2) The lateral surface area of the cone, considering π ≈ 3.14. (3) The total surface area of the cone, considering π ≈ 3.14.