Gold, which has a density of 19.32g/cm^3, is sold by the troy ounce, which is 31.103 g. What is the volume, in cubic centimeters of 1.4 oz t of pure gold?
The Correct Answer and Explanation is :
To find the volume of 1.4 troy ounces of gold, we can use the formula that relates density, mass, and volume:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Rearranging the formula to solve for volume:
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
]
Step 1: Understand the values
- The density of gold is given as (19.32 \, \text{g/cm}^3).
- The mass of gold is (1.4 \, \text{troy ounces}).
- We know that 1 troy ounce = 31.103 grams, so the mass in grams is:
[
\text{Mass} = 1.4 \, \text{oz t} \times 31.103 \, \text{g/oz t} = 43.5442 \, \text{g}
]
Step 2: Calculate the volume
Now, we can plug the mass (43.5442 g) and the density (19.32 g/cm³) into the volume formula:
[
\text{Volume} = \frac{43.5442 \, \text{g}}{19.32 \, \text{g/cm}^3}
]
[
\text{Volume} \approx 2.26 \, \text{cm}^3
]
Final Answer:
The volume of 1.4 troy ounces of pure gold is approximately 2.26 cubic centimeters.
Explanation:
This problem involves understanding the relationship between mass, density, and volume. The key point is that the troy ounce, a unit of mass commonly used for precious metals like gold, is different from the avoirdupois ounce typically used for most other items. Gold is dense, with its mass being concentrated in a relatively small volume. By using the formula for density and rearranging it to solve for volume, we calculated the required volume of 1.4 troy ounces of gold. The unit conversions and formula application helped us determine that the volume of gold is just over 2 cubic centimeters, which is a small but significant amount given the high density of gold.