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
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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