The story
From the fact that floating icebergs typically have about nine tenths of their volume below the surface of the water. Early uses of the term are believed to have been influenced by the sinking of the R.M.S. Titanic on April 15, 1912 after it struck an iceberg. First attested in 1962 in the figurative sense.
Etymology from Wiktionary, CC BY-SA 4.0.