To determine the volume of the gold nugget, given the density and mass, we can use the formula for density [tex]\( D \)[/tex]:
[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 are given:
- The density of gold, [tex]\( D = 19.3 \, \text{g/cm}^3 \)[/tex],
- The mass of the gold nugget, [tex]\( m = 13 \, \text{g} \)[/tex].
We need to find the volume [tex]\( v \)[/tex]. Rearrange the formula to solve for volume:
[tex]\[ v = \frac{m}{D} \][/tex]
Substitute the given values into the equation:
[tex]\[ v = \frac{13 \, \text{g}}{19.3 \, \text{g/cm}^3} \][/tex]
Dividing [tex]\( 13 \)[/tex] by [tex]\( 19.3 \)[/tex] gives:
[tex]\[ v \approx 0.6735751295336787 \, \text{cm}^3 \][/tex]
Given the options provided:
- [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 closest value is:
[tex]\[ v \approx 0.67 \, \text{cm}^3 \][/tex]
Thus, the volume of the 13 g gold nugget is approximately [tex]\( 0.67 \, \text{cm}^3 \)[/tex].
