in architecture, a type of vault or small dome, 1540s, from Italian cupola, from Late Latin cupula "a little tub," diminutive of Latin cupa "cask, barrel" (see cup (n.)). Hence "the rounded top of any structure."
The Italian word signifies a hemispherical roof which covers a circular building, like the Pantheon at Rome or the temple of Vesta at Tivoli. Most modern cupolas are semi-elliptical, cut through their shortest diameter; but the greater number of ancient cupolas were hemispherical. In colloquial use, the cupola is often considered as a diminutive dome, or the name is specifically applied to a small structure rising above a roof and often having the er of a tower or lantern, and in no sense that of a dome. [Century Dictionary, 1897]