Given:

The volume of each cube is 216 cm cube

Formula Used:

Side = ∛ Volume of cube

Lateral surface area of cuboids = 2 × (l + b) × h

Total surface area of cuboids = 2 × (lb + bh + hl)

Calculation:

When three cubes are place side by side so, the breadth and height of resulting cuboids will be same as cube but length will change

∴ Length of cuboid = 6 + 6 + 6 = 18 cm

So, length = 18 cm, breadth = 6 cm and height = 6 cm

∴ Lateral surface area of cuboids = 2 × (18 + 6) × 6 = 288 cm

Now, When two cubes are place side by side so, the breadth and height of resulting cuboids will be same as cube but length will change

∴ Length of cuboid = 6 + 6 = 12 cm

So, length = 12 cm, breadth = 6 cm and height = 6 cm

∴ Total surface area of cuboids = 2 × (12 × 6 + 6 × 6 + 6 × 12) = 360 cm square

Now, the ratio of lateral surface area three cubes placed together to total surface area of all two cube placed together

∴ Required ratio = 288 ∶ 360 = 4 ∶ 5

Hence, option (2) is correct