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Thinking about Geometry

Review question

If a cone sits on this sphere, what 's the cone's volume?
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Ref: R9694

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Question

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.

Calculate

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