Answer:
The volume of a gold piece is[tex]V=16.51 \mathrm{cm}^{3}[/tex]
Explanation:
Given:
Density of pure gold, [tex]D=19.32 \frac{g}{\mathrm{cm}^{3} }[/tex]
Mass of the gold piece, [tex]\mathrm{M}=318.97[/tex]
To Find:
The volume for a piece of gold whose mass is [tex]318.97 g[/tex]
Solution:
The formula for density is:
[tex]D=\frac{M}{V}[/tex]
where,
D is density,
M is mass,
V is volume.
The above formula can be rewriiten as
[tex]V=\frac{M}{D}[/tex]
Substituting the values ,we get
[tex]V=318.97 \mathrm{g} \frac{\mathrm{Au}}{19.32 \frac{\mathrm{g}}{\mathrm{cm}^{3}} \mathrm{Au}}[/tex]
Taking multiplicative inverse of density , we have
[tex]V=318.97 \text { of }Au\frac{1 \mathrm{cm}^{3}\mathrm{Au}}{19.32 \mathrm{of}\mathrm{Au}}[/tex]
[tex]V=318.97\frac{1 \mathrm{cm}^{3}}{19.32}[/tex]
[tex]V=\frac{318.97}{19.32} \mathrm{cm}^{3}[/tex]
[tex]V=16.51 \mathrm{cm}^{3} \mathrm{Au}[/tex]
Result:
Thus the volume of gold piece weighing 318.97 g is[tex]V=16.51 \mathrm{cm}^{3}[/tex]
