IMC 2009 · Problem 1

Let $\ell$ be a line and $P$ a point in $\mathbb{R}^3$. Let $S$ be the set of points $X$ such that the distance from $X$ to $\ell$ is greater than or equal to two times the distance between $X$ and $P$. If the distance from $P$ to $\ell$ is $d > 0$, find the volume of $S$.