cone-shaped vs conic

cone-shaped is not a noun while conic is a noun.

Word	Noun	Adjective	Verb	Adverb
cone-shaped	No	Yes	No	No
conic	Yes	Yes	No	No

As adjectives, cone-shaped and conic are synonyms defined as:

Other synonyms of cone-shaped include conelike, conical.

cone-shaped (noun)	conic (noun)
	(geometry) a curve generated by the intersection of a plane and a circular cone

cone-shaped (adjective)	conic (adjective)
relating to or resembling a cone	relating to or resembling a cone