A Dhaka puzzle: Secrets of a forgotten building

When you come across the age-old artwork titled ‘Part of the Interior of the City of Dacca,’ you may have a number of thoughts in mind, possibly in this order: at first, you will be taken aback by the beauty of the art itself; second, you will marvel on how splendid and different Dhaka looked in the olden times; and third, you may question what that grand, tall building was!

Before we turn our attention to the aforementioned question, let’s put a context first. This artwork is by Sir Charles D’Oyly, civil servant and amateur artist, who was in Dhaka during the British colonial era. It is one of the several portrayals of our city, published in a set of folios called Antiquities of Dacca. This particular artwork was published in 1814 — more than two centuries ago. 
Now, back to our question: what is that prominently displayed multi-storied building? The structure is shrouded in mystery, as there is no definite answer as to what purpose the edifice served. 
The description accompanying the visual in Antiquities of Dacca speculated that the structure was utilised to indicate or measure the height of floods or tides in the region, comparing it to Nilometer of river Nile. 
On the other hand, Syed Muhammed Taifoor, in his book Glimpses of Old Dhaka, said that it was a naobetkhana (a band house or a house from where drums are played).
Whatever it was, the structure seemed to have provided much joy amongst the young of that era and place. According to the description of the visual given in the Antiquities of Dacca, boys used to dive from the different stories of the building into the pool below; the more adventurous ones jumped from the very peak!
What do you think the building actually was?