Correct Answer - Option 4 : 7 : 8
Given:
A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm
where l = 18 cm, b = 36 cm and h = 72 cm
It is melted and recast into 8 cubes of the same volume.
Concept used:
The volume of cuboid = lbh
The total surface area of the cuboid = 2(lb + bh + hl)
Where l = length, b = breadth and h = height
The volume of cube = a3
The lateral surface area of cube = 4 × a2
Where a = side of cube
Explanation:
according to the question,
lbh = 8 × a3
⇒ 18 × 36 × 72 = 8 × a3
⇒ a3 = 18 × 36 × 9
⇒ a = √(9 × 2 × 9 × 2 × 2 × 9)
⇒ a = 18 cm
now,
according to the question,
2(lb + bh + hl) : 8 × 4 × a2
⇒ 2(18 × 36 + 36 × 72 + 72 × 18) : 8 × 4 × (18)2
⇒ 2 × 18 × 36(1 + 4 + 2) : 8 × 4 × 18 × 18
⇒ 36 × 36 × 7 : 32 × 18 × 18
⇒ 7 : 8
∴ The ratio is 7 : 8.