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## 'F'arc'tion' printed from http://nrich.maths.org/

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: $$\frac{3\pi r^2}{4}
\times\frac{1}{6r^2}= \frac{\pi}{8}$$