How did the term "volume" come to be used for the control which adjusts loudness/intensity?
The Oxford English Dictionary gives this earliest cite from 1822: 



It simply referred to "volume of sound", and the latter part got dropped. 

The etymology of the noun "volume" from this source: 


  14c., "roll of parchment containing writing; a bound book," from Old French volume "scroll, book; work, volume; girth, size" (13c.) and directly from Latin volumen (genitive voluminis) "roll (of a manuscript); coil, wreath," literally "that which is rolled," from volvere "to turn around, roll," from PIE root *wel- (3) "to turn, revolve." Meaning "book forming part of a set" is 1520s in English, from that sense in French. Generalized sense of "bulk, mass, quantity" (1620s) developed from that of "bulk or size of a book" (1520s), again following the sense evolution in the French word.