Find the side length of the largest cube which can fit inside a sphere of diameter 24cm.
Clearly the largest cube will touch the circle at each of the eight corners. So start by drawing this, then marking in the radii so that they go from the centre of the sphere and cube to each corner of the cube. Can you see what to do from there?
the largest cube inscribed in a sphere is that with the big diagonal between opposite vertex identical with the diameter of sphere so where l is the side of the cube and d the diameter of the sphere.