Well, that is large in height, but I've seen much larger.

These folks (Nippon Chemi-con) have a super capacitor that is 2.8v 3150F (that is not a type, that is 3,150 Farads) and it is 63.5mm diameter and 172mm tall (~2.5" x 6.75")

Not to be outdone, Chemi-con has a 10,000uF 500v electrolytic cap which is a whopping 89mm x 270mm (3.5" x 10.6") which is much bigger than the one shown above. And even bigger, they have a 29,000uF 450v which is 100mm x 270mm (3.94" x 10.6"). Both of these are in production, but I don't know of any stock in the US...