The cube calculation

Rather than just saying "the surface goes up", we can work out by how much. That is what assignment 17.2 does.

Figure to be added

The cube of limestone 2 cm along each edge, and the shape it makes once it has been cut into 8 small cubes 1 cm along each edge (assignment 17.2).

The problem

A cube of limestone (CaCO₃) 2 cm along each edge is dropped into dilute hydrochloric acid. What surface area does the acid meet? And how does that change if the cube is first cut into 8 smaller cubes?

Working	Result
Area of one face of the cube	2 cm × 2 cm = 4 cm²
Area of all 6 faces	4 cm² × 6 = 24 cm²
Area of one face of a small cube	1 cm × 1 cm = 1 cm²
Area of the 6 faces of one small cube	1 cm² × 6 = 6 cm²
Total surface area of all 8 cubes	6 cm² × 8 = 48 cm²

The result

The same limestone. The same mass. Yet the surface area has doubled, from 24 cm² to 48 cm². Cut the cubes smaller again and it goes higher still.