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But for ice that is not floating, like the vast amounts of ice in Antartica that are thousands of feet thick and rest on the land. When that ice enters the water, the level of the water will rise. Just ask Archimedes.
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Archimedes probably wouldn´t know what would happen with the climate 2300 years later, but with the Southern Hemisphere cooling down this question is highly hypothetical and therefore irrelevent. In fact Antarctica is gaining, which is contributing negative to loss of Arctic ice, a fact rarely mentioned. BTW 90% of Earth ice mass is on Antarctica.