Side of a cube = 12cm
We know volume of cube =
(side)³ = (12)³ = 1728m³
Surface area of cube = 6a² = 6(12)²—————-(i)
The cube is cut into eight small cubes of equal volume.
Let the side of the which is cut into 8 parts be = x
The volume of a small cube = x³
The surface area of a small cube = 6x² —————-(ii)
Volume of each small cube = (1728/8) cm³ = 216 cm³
Or (x)3 = 216 cm³
Or x = 6 cm
Surface areas of the cubes ratios = (Surface area of the bigger cube)/(Surface area of smaller cubes)
From eq (i) and (ii), we get
Surface areas of the cubes ratios
Therefore, the required ratio is 4: 1.
The ratio between their surface areas is 4: 1