Water displacement by two sphere sizes

Core stretch

A cylindrical container has internal diameter \(12\) cm and internal height \(30\) cm. Initially, the water depth is \(20\) cm. Three identical large solid spheres and three identical small solid spheres are held completely below the water surface, and the water depth rises to \(21\) cm. No water is lost. Each large sphere has twice the radius of each small sphere. Ignore the volume of the thin supports.

The schematic diagrams are not drawn to scale. The six spheres are held in a single vertical stack, touching their neighbours, with the lowest sphere touching the base.

1. Find the total volume of the six spheres, giving your answer in terms of \(\pi\).[2]
2. Find the radius of a large sphere.[3]
3. Check that the vertical stack fits inside the container and is completely below the final water surface.[2]