Problem 45548. Pentagonal dodecahedron

Pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges(e).

The only known data is the surface area(A). Specify the volume(V) of the dodecahedron!

Example: A = 200; e = 4.8056; V = 242.1235;