Square pyramid recast into unequal spheres

Core stretch

A right square pyramid has base side 10 cm and height 24 cm.

1. Find its base diagonal.[2]
2. Find a slant edge from vertex to base corner.[2]
3. Find its volume.[2]
4. It is melted into two spheres whose radii are \(r\) and \(2r\). Using \(\pi=3.142\), find \(r\) to 3 significant figures.[2]