Question : A cuboid of sides 12 cm, 18 cm, and 27 cm is melted to form a cube. What is the ratio of the total surface area of the cuboid to that of the cube?
Option 1: $18 : 17$
Option 2: $17 : 19$
Option 3: $19 : 18$
Option 4: $17 : 23$
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Correct Answer: $19 : 18$
Solution :
Volume of cuboid = 12 × 18 × 27 = 5832 cm
3
Let $a$ be the side of a cube.
Volume of cube = $a^3$ = 5832
⇒ $a$ = $\sqrt[3]{5832}$ = 18 cm
Surface area of the cuboid = 2(12 × 18 + 18 × 27 + 27 × 12)
= 2(216 + 486 + 324)
= 2 × 1026
= 2052
Surface area of the cube = 6 × 18 × 18 = 1944
So, the required ratio = $2052 : 1944 = 19 : 18$
Hence, the correct answer is $19 : 18$.
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