A solid cube of side 12 cm is cut into eight cubes of equal volume.

Solution:

Side (a) of cube = 12 cm

Volume of cube $=(a)^{3}=(12 \mathrm{~cm})^{3}=1728 \mathrm{~cm}^{3}$

Let the side of the smaller cube be $a_{1}$.

Volume of 1 smaller cube $=\left(\frac{1728}{8}\right) \mathrm{cm}^{3}=216 \mathrm{~cm}^{3}$

$\left(a_{1}\right)^{3}=216 \mathrm{~cm}^{3}$

$\Rightarrow a_{1}=6 \mathrm{~cm}$

Therefore, the side of the smaller cubes will be 6 cm.

Ratio between surface areas of cubes $=\frac{\text { Surface area of bigger cube }}{\text { Surface area of smaller cube }}$

$=\frac{6 a^{2}}{6 a_{1}^{2}}=\frac{(12)^{2}}{(6)^{2}}$

$=\frac{4}{1}$

Therefore, the ratio between the surface areas of these cubes is 4:1.