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

Solution

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

= (6a²)/(6c²)

= a²/c²

= 122/62 

= 4/1

Therefore, the required ratio is 4: 1.

Answer

The ratio between their surface areas is 4: 1

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