A cuboid of dimensions 18 cm × 12 cm × 8 cm is melted and recast into smaller cubes each having an edge of 4 cm.

Step 1: Surface area of the original cuboid

Surface area of a cuboid = $2(lw + lh + wh)$

$l = 18$, $w = 12$, $h = 8$

$2(18 \cdot 12 + 18 \cdot 8 + 12 \cdot 8) = 2(216 + 144 + 96) = 2 \cdot 456 = 912$ cm²

So, original cuboid’s surface area = 912 cm²

Step 2: Surface area of one small cube

Edge of small cube = 4 cm

Surface area of a cube = $6 \cdot (\text{edge})^2 = 6 \cdot 4^2 = 6 \cdot 16 = 96$ cm²

Step 3: Ratio of one small cube’s SA to cuboid’s SA

Ratio = 96 : 912 = 2 : 19

Answer: 2 : 19