\begin{itemize}
\item sp$^3$ carbon = carbon with four sigma bonds (single bonded).
\item In Buta-1,3-diene (III), all carbon atoms are involved in double bonds or conjugation $\Rightarrow$ No sp$^3$ C.
\item Naphthalene (V) is fully aromatic; all carbon atoms are sp$^2$ hybridized.
\item Acetone (I), Acetic acid (II), and Propyne (IV) each contain at least one sp$^3$ hybridized carbon.
\end{itemize}