A square table (a meter a side) has two spheres on its surface. The spheres have two special properties:

1. The larger is twice the diameter of the smaller, and
2. They are the largest size that will fit on the table without falling off. (They may extend over the edge of the table.)

I. What are the dimensions of the spheres?

II. A third sphere is added next to the other two. What is its largest possible size?