Why did the western powers seek to establish spheres of influence in china?

Western powers seek to establish spheres to influence China because of the vast Markets and railroad opportunities. ... The US wished to attain a strong influence in Cuba to protect American Businesses there.

Protecting and assisting  u.s. citizens  living or traveling abroad; assisting u.s.  businesses  in the international marketplace; coordinating and providing support for international activities of other u.s. agencies (local, state, or federal government), official visits overseas and at home, and other diplomatic efforts.keeping the public informed about u.s. foreign policy and relations with other countries and providing feedback from the public to administration officials.providing  automobile registration  for non-diplomatic staff vehicles and the vehicles of diplomats of foreign countries having  diplomatic immunity  in the united states