Question

Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.

Answer 1

We have,

Edges of the cubes : a₁ = 3 cm, a₂ = 4 cm and a₃ = 5 cm

Let the edge of the new cube be a.

Now,

` "Volume of the new cube" = a_1^3 +a_2^3+a_3^3`

`=>a^3 = 3^3 + 4^3 + 5^3`

⇒ a³ = 27 + 64 + 125

⇒ a³  = 216

`⇒ a = root(3)(216)`

∴ a = 6 cm

So, the edge of the new cube so formed is 6 cm.