Babylonian/Iranian Cisterns have not Fundamentally Changed across the Millenia
A cistern (Persian: āb-anbār) was intended as a large, waterproof reservoir which also allows ventilation and access. The site was chosen as an optimal location to maximize the collection of underground moisture and/or rainwater. The excavation was lined with oven-fired brick set into a sand and clay mixture. It was then covered with a layer (about 3 cm) of waterproof mortar (sārūǰ). Larger cisterns were often lined with an additional double layer of bricks, covered with another layer of sārūǰ of slightly different composition, and finished with a hard plaster coat. The cistern was covered to prevent evaporation and protect the water supply from contamination.
Babylon existed in what is modern day Iran, so Iranian cisterns and Iranian archaeological sites are referenced here. The early history of covered cisterns in Iran has not been studied, although it is possible that a major elaboration of construction techniques may have taken place during the Parthiann and Sasanian periods, when water management constructions (dams, weirs, qanāts) were built extensively.
The above facts are paraphrased from the Encyclopaedia Iranica. Read the full article at http://www.iranicaonline.org/articles/ab-anbar-i-history
As stated in the OP, the cisterns' water volume could take the shape of a rectangular cuboid (like a rectangular tank), a cylinder (like a traditional water well), or other various shapes. The volume of a cistern constructed on a natural aquifer (cave reservoir) would be difficult to calculate. I am not aware of any illustrations/photos of spherical cisterns.