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.

Side of larger cube A = 12 cm. Therefore, volume = A³ = 12 × 12 × 12 = 1728 cm³
According to question, Volume of smaller cube
a³ = Volume of larger cube/8 = 1728 cm³/8 = 216 cm³
⇒ a³ = 216 cm³ ⇒ a = √216 = 6 cm
Hence, the side of new cube is cm.
Now,
ratio of surface areas of two cubes = Surface area of large cube/Surface area of smaller cube = 6A²/6a² = A²/a² = 12²/6² = 144/36 = 4:1