A student has some cubes that are all the same size - OCR - GCSE Maths - Question 10 - 2021 - Paper 3

When cubes are combined, some faces become internal and do not contribute to the total surface area. For four cubes arranged in a way where two are stacked and two are in line, we need to determine how many faces are exposed.

Each cube has 6 faces, so four cubes would initially have:

$Total ~surface ~area ~without ~any ~overlap = 4 \times 54 \text{ cm}^2 = 216 \text{ cm}^2$

However, combining them together, multiple faces will be covered. Typically, when arranged like in the diagram provided, 8 faces are not visible. Therefore, we subtract:

$Each ~hidden ~face = 2 \text{ faces} (from ~the ~stack) \times 2 \text{ cubes} = 4$

So, the remaining surface area:

$Surface ~area = 216 \text{ cm}^2 - (4 \times 9 \text{ cm}^2) = 216 \text{ cm}^2 - 36 \text{ cm}^2 = 180 \text{ cm}^2$

The surface area of the shape made by combining the four cubes is

180 cm².