1560s, "A solid generated by the revolution of a right-angled triangle upon one of its sides as an axis" [Century Dictionary], from French cone (16c.) or directly from Latin conus "a cone, peak of a helmet," from Greek konos "cone, spinning top, pine cone," which is perhaps from a PIE root *ko- "to sharpen" (source also of Sanskrit sanah "whetstone," Latin catus "sharp," Old English han "stone"), but Beekes considers it likely a Pre-Greek word.
There is a use from c. 1400 as "angle or corner of a quadrant," from Latin. From 1560s as "dry, cone-shaped fruit of the pine;" from 1771 as "hill surrounding the crater of a volcano; 1867 as "minute structure in the retina of the eye;" by 1909 as "a conical wafer to hold ice-cream." Cone-shell is from 1770, so called for its shape; cone-flower is from 1822, so called for its conical receptacles.
Probably the greatest "rage" of the year in the eating line has been the ice cream cone. The craze has known no section, although the Middle West has eaten more than any other section, and the South has yet to acquire the habit. As a result of this craze hundreds of cone factories have sprung up, and every one has made large profits. Thus an important side line has come to the fore in aid of the ice cream industry. [The Ice Cream Trade Journal, October 1909]