When the length, the width and the thickness are equally significant, as shown in Figure 9, we need to consider the expansion of the solid in three dimensions. In this case, all the three lengths experience significant changes in length with a change in temperature ΔT.

The change in volume ΔV of an object subjected to a temperature change ΔT is given by

ΔV = γV_cΔT

Using ΔV = V - V₀ and passing through some rearrangements, we have

V = V₀ (1+ V₀)

where V₀ and V are original and final volumes, respectively; γ is the coefficient of volume expansion of the block.