Calculating Volumes via Cylindrical Shells

Let $T$ be a triangle with vertices at $(1003,0)$, $(1004,3)$, and $(1005, 1)$ in the $xy$-plane. Let $V$ be the volume of the solid obtained by revolving $T$ all the around the $y$-axis. Find $V/\pi$.

Source: HMMT February 2006

Hint: You may find some knowledge about center of mass helpful.