A cube of side 4cm is cut into 1cm cubes. What is the ratio of the surface areas of the original cubes and the cut-out cubes?

The cube has side = 4 cm, as shown below:

Now, the cube is cut into small cubes of each side cm.

The total number of cubes = 4 × 16 = 64 small cubes.

Numbers of cut-out cubes =

Now, surface area of cut-out cubes = 64 × 6 × 1 cm²

And surface area of the original cube = 6 × 4²

The required ratio = = 1:4