Chequered Cuboid

Consider the different faces of this cuboid. The faces on the ends of the cuboid will look like these diagrams on the right. Between them they have $9$ black squares and $9$ white squares.






The other four faces all look like the diagram to the right. This contains $6$ white squares and $6$ black squares.

Therefore, between the four faces there are $6 \times 4 = 24$ white squares and $6 \times 4 = 24$ black squares.




Therefore, overall there are $9+24=33$ white squares and $9+24=33$ black squares, so $\frac{1}{2}$ of the squares are coloured black.