Here is the solution from Christiane Eaves, Alicia Maltby, Kathy Lam, Rachael Evans & Fiona Conroy (Y10) The Mount School,York: "

The total surface area of the cube is 6r². The area shaded on one face is

πr2 4

so the total shaded area is

3πr2 4

.

The fraction of the total surface area shaded is thus

3πr2) 4

divided by 6r² which is:

3πr2 4 ×  1 6r2 =  π 8