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To calculate the density of the gold ring, you can use the formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
In this case, the mass is 15.83 grams and the volume is 0.82 milliliters.
Plugging in the values:
\[ \text{Density} = \frac{15.83 , \text{grams}}{0.82 , \text{milliliters}} \]
Now, performing the calculation:
\[ \text{Density} = 19.32 , \text{grams per milliliter} \]
So, the density of the gold ring is approximately 19.32 g/mL.
To calculate the density of the gold bar using the formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Given that the mass of the gold bar is 1,000 grams and the volume is 51.8 milliliters, we can substitute these values into the formula:
\[ \text{Density} = \frac{1,000 , \text{grams}}{51.8 , \text{milliliters}} \]
Now performing the calculation:
\[ \text{Density} \approx 19.31 , \text{grams per milliliter} \]
Thus, the density of the gold bar is approximately 19.31 g/mL.
To compare the densities of the gold ring and the gold bar:
While the densities are very close, they are slightly different. The gold ring has a density of 19.32 g/mL, and the gold bar has a density of 19.31 g/mL. This minor difference may be due to slight variations in composition or air pockets in the ring compared to the bar. In practical terms, however, they are quite similar and could be considered to have nearly the same density, as both densities are consistent with the known density of pure gold, which is approximately 19.32 g/mL.
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