A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Given, side of a cube = 12cm

We know that, formula to find volume of cube = (Side)³  and formula to surface area = 6(side)²

V = (12)³ = 1728 cm³

SA = 6(12) ² = 864 cm²

The cube is cut into eight small cubes of equal volume, let new side be a.

The volume of a small cube = a³

Surface area = 6a² 

Volume of each small cube = 1728/8 = 216 cm³

So here we have, a³ = 216 which implies, a = 6 cm

So here SA of Cube = 6(6)³

Now, the ratio of surface areas of the cube = SA of bigger cube / SA of smaller cubes

Surface areas of the cubes ratios = 6(12)²/6(6)² = 12²/6² = 4

Therefore, the required ratio is 4: 1.