To determine the density of a gold cube given its side length and mass, follow these steps:
1. Calculate the Volume of the Cube:
The volume [tex]\( V \)[/tex] of a cube can be found using the formula for the volume of a cube:
[tex]\[
V = \text{side length}^3
\][/tex]
Given the side length of the cube is 1.55 cm, we can substitute this value into the formula:
[tex]\[
V = 1.55^3 \, \text{cm}^3
\][/tex]
Performing this calculation, we obtain:
[tex]\[
V = 3.723875 \, \text{cm}^3
\][/tex]
2. Calculate the Density of the Gold Cube:
The density [tex]\( \rho \)[/tex] of a substance is defined as its mass [tex]\( m \)[/tex] divided by its volume [tex]\( V \)[/tex]:
[tex]\[
\rho = \frac{m}{V}
\][/tex]
With the given mass of the gold being 71.9 g and the volume we calculated as 3.723875 cm³, we substitute these values into the formula for density:
[tex]\[
\rho = \frac{71.9 \, \text{g}}{3.723875 \, \text{cm}^3}
\][/tex]
Performing this division, we get:
[tex]\[
\rho = 19.307844651069114 \, \text{g/cm}^3
\][/tex]
Thus, the density of the given gold cube is approximately [tex]\( 19.31 \, \text{g/cm}^3 \)[/tex].
