A precise micro-sensor measures the relative volume $V$ of a specialized crystal alloy as it undergoes temperature changes $T$. The relationship is modelled by the formula $V(T)=\sqrt[3]{1+pT}$, where $p$ is a constant. The binomial expansion of $V(T)$ in ascending powers of $T$, up to the term in $T^3$, is $1+\frac{1}{6}T+C{T}^2+D{T}^3$ for $|pT|<1$.