Question : The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm2, 96 cm2 and 144 cm2. It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm2) of 3 such cubes?
Option 1: 648
Option 2: 432
Option 3: 576
Option 4: 288
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Correct Answer: 432
Solution : Let the side of the new cube be $a$. Square of the volume of a cuboid = Product of areas of three adjacent faces of the cuboid According to the question, $\Rightarrow 8a^3\ =\ \sqrt{\left ( 216\ \times 96\ \times 144 \right )}$ $\Rightarrow 8a^3\ =\ 6\ \times 6\ \times 4\ \times 12$ $\Rightarrow a\ =\ 6$ Lateral surface area of each cube $=4\times 6^2 = 144$ sq cm $\therefore$ Lateral surface area of 3 such cubes $=3 \times 144 = 432$ sq cm Hence, the lateral surface area of 3 such cubes is 432.
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