The picture is misleading. It's 310mm long, which is about 12.25 inches. Bought mine from unit pack power's aliexpress outlet.It came with a holder, which was larger in diameter and stronger than your typical light weight bottle holder. EVen then, it's not that secure. I added a second holder. If you supply your own, an old steel frame bottle holder would work best, but I've not seen any for sale.
I would estimate that a 48V 7AH battery would run my Q100 bike for 25-30 miles at 14 mph with pedal assist. We get over 30 miles on a 36V 9AH battery (not the bottle battery).