  Let $K$ be a compact convex set and $m$ be a positive integer. The covering
functional of $K$ with respect to $m$ is the smallest $\lambda\in[0,1]$ such
that $K$ can be covered by $m$ translates of $\lambda K$. Estimations of the
covering functionals of convex hulls of two or more compact convex sets are
presented. It is proved that, if a three-dimensional convex body $K$ is the
convex hull of two compact convex sets having no interior points, then the
least number $c(K)$ of smaller homothetic copies of $K$ needed to cover $K$ is
not greater than $8$ and $c(K)=8$ if and only if $K$ is a parallelepiped.
