I'll give you my game plan.
I'd give you a complete solution, but it's getting late.
I can work on it tomorrow . . . *yawn*
Three spheres with the radius R are lying on a plane, so that they all tangent each other.
A fourth sphere, also with the radius of R, are lying upon the three others,
so that a pyramid os fomed.
Compute the length between the center of the fourth sphere to the underlying plane.
The centers of the four spheres form a regular tetrahedron of edge
The top vertex of the tetrahedron is the center of the fourth sphere.
The bottom vertices of the tetrahedron are the centers of the lower spheres.
These centers are units from the plane.
We need only the altitude of the regular tetrahedron.
Can you finish it now?