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A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

F'arc'tion

Age 14 to 16 Short
Challenge Level

Here is the solution from Christiane Eaves, Alicia Maltby, Kathy Lam, Rachael Evans andFiona Conroy (Y10) The Mount School,York:
Cube
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: $$\frac{3\pi r^2}{4} \times\frac{1}{6r^2}= \frac{\pi}{8}$$
You can find more short problems, arranged by curriculum topic, in our short problems collection.