Every ball in a normed space is convex

Prove that if $V$ is a normed vector space, $f \in V$, and $r > 0$, then the open ball $B(f, r)$ centered at $f$ with radius $r$ is convex.

Prove that any ball in a normed space $X$ is convex.

Prove that the unit ball (open or closed) is convex in every normed linear space.