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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. $468 \pi$
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