Consider the hemi-spherical tank of radius $13 \: m$ as shown in the figure (not drawn to the scale). What is the valume of water (in $m^3$) when the depth of water at the centre of the tank is $6 \: m$?

1. $78 \pi$
2. $156 \pi$
3. $396 \pi$
4. $468 \pi$