cost vs require

cost is a noun but require is not a noun.

Word	Noun	Adjective	Verb	Adverb
cost	Yes	No	Yes	No
require	No	No	Yes	No

As verbs, require is a hypernym of cost; that is, require is a word with a broader meaning than cost:

Other hypernyms of cost include ask, call for, demand, involve, necessitate, need, postulate, take.

cost (noun)	require (noun)
the property of having material worth (often indicated by the amount of money something would bring if sold)
value measured by what must be given or done or undergone to obtain something
the total spent for goods or services including money and time and labor

cost (verb)	require (verb)
be priced at	make someone do something
require to lose, suffer, or sacrifice	consider obligatory; request and expect
	have need of
	require as useful, just, or proper