Chequered Cuboid
A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?
Problem
Image
What fraction of the surface area of the cuboid is coloured black?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Image
Image
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.