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

The total surface area of the cube is $ 6r^2. $ The area shaded on one face is $ \frac{\pi r^2}{4}$ so the total shaded area is $ \frac{3\pi r^2}{4}.$

The fraction of the total surface area shaded is thus $\frac{3\pi r^2}{4}$ divided by $6r^2$ which is: $$\frac{3\pi r^2}{4} \times\frac{1}{6r^2}= \frac{\pi}{8}$$