Question 7
(GDR) A sphere is inscribed in a regular cone. Around the sphere a cylinder is circumscribed so that its base is in the same plane as the base of the cone. Let $V_1$ be the volume of the cone and $V_2$ the volume of the cylinder.
(a) Prove that $V_1=V_2$ is impossible.
(b) Find the smallest $k$ for which $V_1=kV_2$, and in this case construct the angle at the vertex of the cone.
(a) Prove that $V_1=V_2$ is impossible.
(b) Find the smallest $k$ for which $V_1=kV_2$, and in this case construct the angle at the vertex of the cone.