The density of gold is [tex]19.3 \, \text{g/cm}^3[/tex]. What is the volume of a 13 g gold nugget? (Density: [tex]D=\frac{m}{v}[/tex])

A. [tex]0.25 \, \text{cm}^3[/tex]
B. [tex]0.67 \, \text{cm}^3[/tex]
C. [tex]1.48 \, \text{cm}^3[/tex]
D. [tex]2.50 \, \text{cm}^3[/tex]



Answer :

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].