A cubic crystal of titanium dioxide catalyst, used in solar-milled water purification, has six square faces. The dimensions of this large catalyst block are 20 mm×20 mm×20 mm20\text{ mm} \times 20\text{ mm} \times 20\text{ mm}20 mm×20 mm×20 mm.
To increase its catalytic activity, the block is finely milled into 100010001000 identical smaller cubes, each of dimensions 2 mm×2 mm×2 mm2\text{ mm} \times 2\text{ mm} \times 2\text{ mm}2 mm×2 mm×2 mm.
Calculate:
The total surface area of the original large block.
The total surface area of the 100010001000 smaller cubes combined.
The ratio of the combined surface area of the 100010001000 smaller cubes to the surface area of the original block.
3 exam-style questions on AQA GCSE Chemistry 2.4 Bulk and surface properties of matter including nanoparticles, covering 2.4.1 Sizes of particles and their properties and 2.4.2 Uses of nanoparticles. Each one has a worked solution and a mark scheme showing where the marks go.