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Two cubes are joined to form a cuboid. If the total surface area of the cuboid thus formed is 640 cm², then what is the length of the edge of the cube?

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12 cm

10 cm

8 cm

6 cm

answer is B.

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Detailed Solution

Let the length of the edge of the cube be a

Two cubes are joined to form a cuboid

Then, the length l of the cuboid = 2a

breadth (b) of the cuboid = a

height (h) of the cuboid = a

The total surface area of a cuboid is given by 2 (lb + bh + lh).

640 cm² = 2 (2a x a + a x a + 2a x a)

⇒ 640 cm² = 2 (2a² + a² + 2a²)

⇒ 10 a² = 640 cm²

⇒ a² = 64 cm²

⇒ a = 8 cm

Thus, the length of the edge of the cube is 8 cm.

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