The United States took a larger role in world affairs through the projection of its military and economic power. It did so in order to become a more important country.
By the late 1800s, the United States was big enough and strong enough to want to play a greater role in international affairs. It saw European countries controlling large empires and it wanted to be considered the equal of those countries. It felt that it deserved to be a great power in the world. In addition, the US wanted to play a greater role in the world for economic reasons. It wanted to be able to have more control over other countries so as to get economic benefits (as with the Open Door policy in China or the “opening” of Japan).
In order to get more power, the US used military and economic might. It used military might in such instances as the Spanish-American War, many interventions in small Caribbean countries, and the two world wars. For example, by using the military to take Cuba and the Philippines from Spain, the US took a larger role in the world. It did so again after WWII when its military might helped defeat the Axis and set the US up as the most powerful free nation in the world.
The US also used its economic might to take a larger role in world affairs. For example, it used “Dollar Diplomacy” to get more of a say in the affairs of its neighbors. Later on, it used the Marshall Plan to give it more influence in Western Europe.
In these ways, the US used military and economic power to take a larger role in international affairs. It did so in order to be reckoned as a great power.