Let the edges of cubes be a₁, a₂ and a₃

So, a₁ = 3 cm, a₂ = 4 cm, and a₃ = 5 cm

Explanation: Here the sum of volumes of all three cubes will be equal to the volume of the resulting larger cube as the resulting cube is formed by melting the three cubes.

Volume of cube with edge a₁ = v₁ = (a₁)³

⇒v₁ = (3)³

∴ v₁ = 27 cm³→eqn1

Similarly

Volume of cube with edge a₂ = v₂ = (a₂)³

⇒v₂ = (4)³

∴ v₂ = 64 cm³→eqn2

Volume of cube with edge a₃ = v₃ = (a₃)³

⇒v₃ = (5)³

∴ v₃ = 125 cm³→eqn3

Now let the volume of resulting cube be ‘V’ cm³

So, V = v₁ + v₂ + v₃

⇒ V = 27 + 64 + 125 (from eqn1, eqn2 and eqn3)

∴ V = 216 cm³→eqn4

Let the edge of resulting cube be ‘a’ cm

So, volume of the resulting cube = V = a³→eqn5

Equate equation 4 and 5,

⇒ a³ = 216

⇒ a = ∛(216)

∴ a = 6 cm

The edge of new cube formed is 6 cm.