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What method could you use to determine the volume of a sphere, or of any object?...

What method could you use to determine the volume of a sphere, or of any object? Explain how Archimedes could have determined if his kings crown is indeed made of pure gold while taking a bath at the same time?
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Answer #1

To determine the volume of a sphere or of any object, completely immerse the object in a bucket filled with water. Collect the water that overflows when the object is completely immersed in water. The volume of this water will be equal to the volume of the object.

Archimedes can initially weigh the crown and keep a note of its weight. Then when the king takes bath ask him to immerse fully the crown in the tub filled with water and collect the water that overflows. Archimedes can then calculate the volume water that overflowed and multiply it by the density of gold. This should give archimedes the same value as he had noted earlier else the crown isn't made of pure gold.

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