Question
If Archimedes' crown had a mass of $1 \mathrm{kg}$ and a volume of $120 \mathrm{cm}^{3},$ was the crown made of pure gold? Explain.
Step 1
The density of an object is calculated by dividing its mass by its volume. In this case, the mass of the crown is 1 kg and the volume is 120 cm³. The formula for density is: \[Density = \frac{Mass}{Volume}\] Show more…
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You, Archimedes, suspect that the king's crown is not solid gold but is instead goldplated lead. To test your theory, you weigh the crown, and find it to weigh 60.0 N and to have an apparent weight of 56.2 N when it is completely submerged in water. What is the density of the crown? 15789.5 kg/m^3 19300 kg/m^3 11300 kg/m^3 7500 kg/m^3
Archimedes' principle was being stated when Archimedes of Syracuse tested the crown of King Hieron II. The crown has a mass of 13.4 kg but when submerged in water, an accurate scale reads only 12.1 kg. Is the king's crown made of gold?
Archimedes purportedly used his principle to verify that the king's crown was pure gold by weighing the crown submerged in water. Suppose the crown's actual weight was $25.0 \mathrm{N}$. What would be its apparent weight if it were made of (a) pure gold and (b) $75 \%$ gold and $25 \%$ silver, by volume? The densities of gold, silver, and water are $19.3 \mathrm{g} / \mathrm{cm}^{3}, 10.5 \mathrm{g} / \mathrm{cm}^{3},$ and $1.00 \mathrm{g} / \mathrm{cm}^{3},$ respectively.
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