In this note, the following question, not discussed well in the literature, is considered: $$ \text{Is the convex hull of } A \text{ closed if } A \text{ is a closed cone in } R^n?$$ When $n = 1$ or $2$, the answer to the above problem is affirmative. The main purpose of this brief note is to give a simple example showing that the answer is negative when $n\geq 3$.