Final answer:
Option (c), Cyrus the Great became the ruler of the Persian Empire by leading a rebellion against the Medians in 550 BCE, subsequently defeating the Neo-Babylonian Empire in 539 BCE.
Step-by-step explanation:
Cyrus the Great became the ruler of the Persian Empire through military conquest and tactical alliances. In 550 BCE, Cyrus led the Persians in rebellion against the ruling Medians, leading to the overthrow of the Median dynasty. Cyrus's strategy included integrating the Median elite into his government, thus effectively founding the powerful Achaemenid dynasty and expanding the empire through a series of campaigns.
Following the defeat of the Medes, Cyrus conquered Lydia and the Greek colonies in Ionia, treating the conquered people with fairness to minimize uprisings. His conquests culminated in 539 BCE with the successful invasion of the Neo-Babylonian Empire, after which he integrated the Babylonian territories into his empire and maintained control through the selection of local governors.
Although Cyrus's leadership was a combination of both inherited power and military strength, the most accurate answer to how he became the ruler of the Persian Empire is through his initial conquest over the Median dynasty and subsequent military campaigns.