To determine the volume of a gold nugget with a mass of 13 grams and a density of [tex]\(19.3 \, \text{g/cm}^3\)[/tex], we can use the formula for density, which is:
[tex]\[ D = \frac{m}{v} \][/tex]
where:
- [tex]\(D\)[/tex] is the density,
- [tex]\(m\)[/tex] is the mass,
- [tex]\(v\)[/tex] is the volume.
We need to rearrange the formula to solve for the volume [tex]\(v\)[/tex]. This can be done by isolating [tex]\(v\)[/tex]:
[tex]\[ v = \frac{m}{D} \][/tex]
Given:
- [tex]\(m = 13 \, \text{g}\)[/tex],
- [tex]\(D = 19.3 \, \text{g/cm}^3\)[/tex],
we substitute these values into the equation:
[tex]\[ v = \frac{13 \, \text{g}}{19.3 \, \text{g/cm}^3} \][/tex]
By performing the division, we get:
[tex]\[ v = 0.6735751295336787 \, \text{cm}^3 \][/tex]
Hence the volume of the 13-gram gold nugget is approximately [tex]\(0.67 \, \text{cm}^3\)[/tex] when rounded to two decimal places, which matches one of the provided options.
Answer: The volume of the 13-gram gold nugget is [tex]\(0.67 \, \text{cm}^3\)[/tex].
