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He was asked to find out wether a goldsmithe had cheated the king

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Q: What problem was Archemides asked to solve for King Hiero of Syracuse?
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What problem did king hiero want Archimedes to solve?

During Archimedes' time in Syracuse, King Hieron, the king of Syracuse and a close friend of Archimedes, commissioned the construction of a beautiful golden crown. When the goldsmith returned the crown, the king suspected him of stealing some of the gold and replacing it in the crown with silver. The king wanted to make sure that he got all of his gold back, so he asked Archimedes to discover the true contents of the crown.


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