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?

Let the length of the edge of the cube be a.

Then, the length l of the cuboid = 2a

Breadth, b of the cuboid = a

Height, h of the cuboid = a

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

∴ 640 cm² = 2 (2a.a + a.a + 2a.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.