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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


Team Careers360 18th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

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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