The density of gold is [tex]$19.3 \, g/cm^3$[/tex]. What is the volume of a 13 g gold nugget?

(Density: [tex]D = \frac{m}{v}[/tex])

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



Answer :

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].