Answer :
Final answer:
To determine if the crown is made of pure gold, we can calculate its density and compare it to the density of gold.
Explanation:
According to the lore of ancient Greece, Archimedes discovered the displacement method of density determination while bathing and used it to find the composition of the king's crown. If a crown weighing 4 lb 13 oz displaces 186 mL of water, we can determine its density and compare it to the density of gold to find out if it is made of pure gold.
To calculate the density of the crown, we can use the formula density = mass/volume. First, we need to convert the weight of the crown to mass. Since 1 lb is approximately 453.6 grams and 1 oz is approximately 28.35 grams, the mass of the crown is (4 lb + 13 oz) x 453.6 g/lb + 13 x 28.35 g/oz. The volume of the crown is given as 186 mL. By dividing the mass by the volume, we can calculate the density of the crown.
If the density of the crown is equal to the density of gold (19.3 g/cm³), then the crown is made of pure gold. Otherwise, it is made of a different material.
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