Answer:

Step-by-step explanation:
Let's establish the historical context and meanings of the two terms here to start us off.
CONTEXT
- Industrialization was the American shift in the economy towards machines, factory production, and greater production of goods for profit. This was a major shift from the agricultural society of the Old America and flourished in New England to help grow the economy to great heights. The first and second Industrial Revolution exemplified these changes as businesses, corporations, and machines advanced the economy.
- Imperialism was America opening its arms to foreign countries and America becoming an imperial power just like the European nations. Examples of American Imperialism include the conquest of the Phillippines, Cuba, Puerto Rico, and Hawaii. These moves, most importantly, elevated America to a world power and established its dominance among the other powerful European nations. These moves were often criticized as Anti-Imperialists believed America was departing from its founding Republic ideals - an escape from an empire.
Now, we must examine the relationship between the economy and world power.
ECONOMY AND POWER
A key question to ask yourself when considering Imperialism and its causes is "What makes a great nation powerful?" Britain, for example, had lots of territories and an extremely powerful army which secured itself as a world power.
However, what exactly ascended America to world power status? It wasn't just the military, and it wasn't just the social issues.
What set America apart was its new and modern economy. Industrial economy and its effects on the American riches soared economic levels to never seen before heights. When your country is doing that well and you have that much money, you have the power to do a lot of things. Thus, America's ascent to being a world power rose through the new Industrial economy.
Imperialism, as described earlier, was America's rise to world power as they claimed territory overseas. The massive increase in economic prosperity allowed America to reach these distances. Its importance in international affairs allowed it to amass an army capable of taking places such as the Phillippines. The attached political cartoon is a great example of this. America ascends from its baby-like isolationist state to a great power with the hands of major powers looking to do business.
Thus, in short, Industrialization fueled the way for a powerful economy. This economy brought forth a powerful and rich nation which was capable of expanding overseas.
An important historical concept here is causation (one of the key APUSH principles - good luck on your AP exam if you're taking it!). Causation is key to understanding the causes, and effects, of historical situations throughout American history.
Hope this helped!