To solve for the volume of a gold nugget given its density and mass, we can use the formula for density:
[tex]\[ D = \frac{m}{v} \][/tex]
where [tex]\( D \)[/tex] is the density, [tex]\( m \)[/tex] is the mass, and [tex]\( v \)[/tex] is the volume. Rearranging this formula to solve for volume [tex]\( v \)[/tex], we get:
[tex]\[ v = \frac{m}{D} \][/tex]
Given:
- The density of gold ([tex]\( D \)[/tex]) is [tex]\( 19.3 \, \text{g/cm}^3 \)[/tex].
- The mass of the gold nugget ([tex]\( m \)[/tex]) is [tex]\( 13 \, \text{g} \)[/tex].
Now, plug in the given values:
[tex]\[ v = \frac{13 \, \text{g}}{19.3 \, \text{g/cm}^3} \][/tex]
Performing the division, we find:
[tex]\[ v \approx 0.6735751295336787 \, \text{cm}^3 \][/tex]
Therefore, the volume of the 13-gram gold nugget is approximately [tex]\( 0.67 \, \text{cm}^3 \)[/tex].
Among the given options:
- [tex]\( 0.25 \, \text{cm}^3 \)[/tex]
- [tex]\( 0.67 \, \text{cm}^3 \)[/tex]
- [tex]\( 1.48 \, \text{cm}^3 \)[/tex]
- [tex]\( 2.50 \, \text{cm}^3 \)[/tex]
The correct choice is:
[tex]\[ \boxed{0.67 \, \text{cm}^3} \][/tex]
