This ratio arises because volume is composed of three mutually orthogonal directions. Thus, in an isotropic material, for small differential changes, one-third of the volumetric expansion is in a single axis. As an example, take a cube of steel that has sides of length L. The original volume will be V = L 3 and the new volume, after a temperature increase, will be V + Δ Δ V = ( L + Δ Δ L ) 3 = L 3 + 3 L 2 Δ Δ L + 3 L Δ Δ L 2 + Δ Δ L 3 ≈ ≈ L 3 + 3 L 2 Δ Δ L = V + 3 V Δ Δ L L .