A sphere of radius \(\quantity{6}{cm}\) fits inside a cone of vertical angle \(84^\circ\), so that \(BA\) is a tangent to the sphere.

The sphere and cone described in the question; the point $B$ is the apex of the cone and $A$ lies on the intersection between the sphere and the base circle of the cone.


  1. the length \(AB\);
  2. the radius of the base of the cone;
  3. the shortest distance from \(B\) to the sphere;
  4. the volume of the cone.