Depends to some degree on the type of arowana. Silvers are much more elongated than jardini and would be treated appropriately in a tank that is at least 72x36 if we are talking about standard sizes. A wide cylinder could also work. As for jardini, you could go 72x30.
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One rule of thumb (and I know ther are many) is that the minimum tank size for any fish is 6X length, X 2X width, 1X height. So, assuming an adult length of 36", roughly 18' X 6' X 3' (1,616 gallons) at adulthood. To put things in perspective, this would be equal to keeping a 1" neon tetra in a 6" X 3" X 1" tank (1/10th of one gallon), so this number is an absolute minimum since I doubt many of us would attempt to maintain a one inch fish in a 1/10th of a gallon aquarium.
-Shane
Aquatic Obsession in Manssas has one in their HUGE tank housed with a really really big pacu. I go say hi to both of them every time I'm in there. Pacu has the most interesting face, almost human like.