Short answers, pulled from the story.
Hiero II was a Greek ruler of Syracuse in Sicily who reigned from 275 to 215 BC. He was the illegitimate son of a Syracusan noble named Hierocles and had served as a general under Pyrrhus of Epirus before rising to power. He is notable for his long loyalty to Rome during the Punic Wars and for employing Archimedes.
Hiero II asked his kinsman Archimedes to determine whether a goldsmith had cheated him by substituting silver for gold in a votive crown. Archimedes discovered the principle of water displacement while stepping into a bath and allegedly ran naked through Syracuse shouting "eureka, eureka!" The method successfully proved the goldsmith had committed fraud, as recorded by the Roman writer Vitruvius.
After Pyrrhus left Sicily in 275 BC, the Syracusan army and citizens appointed Hiero commander-in-chief. He was proclaimed king by his troops following a victory over the Mamertines in 265 BC. Between 275 and 271 BC he consolidated total power in the city by aligning with the demos and ruling within the law rather than through purges.
In 263 BC, Hiero concluded a treaty with Rome under which he retained authority over the south-eastern portion of Sicily and the eastern coastline as far as Tauromenium. He remained loyal to Rome under this arrangement until his death, supplying Roman forces with men and provisions throughout the Punic conflict.
Hiero II died shortly after the Battle of Cannae in 216 BC. He was born around 308 BC and ruled Syracuse from 275 to 215 BC, making his reign one of the longest in the city's history.
In Chapter 6 of The Prince, written in the 16th century, Machiavelli cited Hiero II as an exceptionally virtuous man and a rare example of someone who rose to princely power from being a private individual. Machiavelli placed Hiero alongside Moses, Cyrus, Theseus, and Romulus as models of this kind of ascent.