To determine the volume of a gold nugget given its mass and density, we will use the density formula and solve for the volume.
The formula for density 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.
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 solve for the volume [tex]\( v \)[/tex]. Rearranging the density formula to solve for volume, we get:
[tex]\[ v = \frac{m}{D} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ v = \frac{13 \, \text{g}}{19.3 \, \text{g/cm}^3} \][/tex]
Performing the division:
[tex]\[ v \approx 0.6735751295336787 \, \text{cm}^3 \][/tex]
Therefore, the volume of the [tex]$13 \, \text{g}$[/tex] gold nugget is approximately:
[tex]\[ 0.67 \, \text{cm}^3 \][/tex]
Among the multiple-choice 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 correct answer is:
[tex]\[ 0.67 \, \text{cm}^3 \][/tex]
