Question : A solid metallic cuboid of dimensions 12 cm × 54 cm × 72 cm is melted and converted into 8 cubes of the same size. What is the sum of the lateral surface areas (in cm2) of 2 such cubes?
Option 1: 2268
Option 2: 1944
Option 3: 2592
Option 4: 3888
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Correct Answer: 2592
Solution :
Volume of Cuboid = l × b × h, where
l = length
b = breadth
h = height
Volume of Cuboid = l × b × h = 8 × a
3
where 'a' is the side of the cube
⇒(12 × 54 × 72) = 8 × a
3
⇒ (12 × 54 × 9) = a
3
⇒ a
= $\sqrt{5832}$ = 18
Lateral surface area of two sides = (4 × 4a
2
) = 8a
2
= 8 × 18 × 18 cm
2
= 2592 cm
2
Hence, the correct answer is 2592.
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