30. Describe a regular tetrahedron around a sphere of radius $R$ and find its volume.
30. To describe a regular tetrahedron around a sphere, we inscribe a regular tetrahedron in it and draw planes through its vertices parallel to the opposite faces. These planes are perpendicular to the radii leading to the vertices and therefore touch the sphere. The intersection of these four planes results in a tetrahedron similar to the given one, since upon rotation by angles $\frac{2 \pi}{3}$ around the symmetry axes of the inscribed tetrahedron, the tangent planes coincide with each other, i.e., all faces and polyhedral angles of the circumscribed tetrahedron are congruent. The distance from the center of this tetrahedron to its face is three times greater than the same distance for the inscribed tetrahedron. Therefore, its volume is 27 times greater than the volume of the inscribed tetrahedron: $V=8 R^{3} \sqrt{3}$ (see problem 28).