To find the volume of a 13 g gold nugget, knowing that the density of gold is [tex]\( 19.3 \, \text{g/cm}^3 \)[/tex], we use the formula for density [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 volume [tex]\( v \)[/tex]:
1. Starting with the density formula:
[tex]\[ D = \frac{m}{v} \][/tex]
2. Rearrange to solve for volume [tex]\( v \)[/tex]:
[tex]\[ v = \frac{m}{D} \][/tex]
3. Substitute the given values into the equation:
[tex]\[ v = \frac{13 \, \text{g}}{19.3 \, \text{g/cm}^3} \][/tex]
4. Calculate the volume:
[tex]\[ v = 0.6735751295336787 \, \text{cm}^3 \][/tex]
Therefore, the volume of a 13 g gold nugget is approximately [tex]\( 0.67 \, \text{cm}^3 \)[/tex].
Looking at the provided 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 answer is [tex]\( 0.67 \, \text{cm}^3 \)[/tex].
