A right circular cone is inscribed in a sphere, as shown. (a) The sphere has centre O and radius 12 cm. A is the vertex of the cone, B is a point on the base of the cone that touches the sphere and, C is the centre of the base of the cone. :0 Let |OC|=x. Find | BC|, the radius of the cone, in terms of x. (i) Show that the volume of the cone is equal to (12 + x)(12 x). (ii) (iii) Hence find the maximum volume of the cone, in terms of T.