To find the density, we need to know the value of mass and volume. We can find the volume of the cube, using the formula of cube's volume:
[tex]\text{Volume of a cube=a}\cdot a\cdot a=a^3.[/tex]
Where a is the value of side, in this case, is 15.6 mm:
[tex]\text{Volume}=15.6mm\cdot15.6mm\cdot15.6mm=15.6^3mm^3=3796.416mm^3.[/tex]
Now, let's convert the volume from mm^3 to cm^3. Remember that 1 cm^3 equals 1000 mm^3:
[tex]3796.416mm^3\cdot\frac{1cm^3}{1000mm^3}=3.796cm^3\approx3.80cm^3.[/tex]
And we can replace the data that we have in the formula of density:
[tex]\begin{gathered} \text{density}=\frac{mass}{volume}, \\ \text{density}=\frac{4.20\text{ g}}{3.80cm^3}, \\ \text{density}=1.105\text{ }\frac{g}{cm^3}\approx1.11\frac{g}{cm^3}. \end{gathered}[/tex]
The answer is that the density of the cube of aluminum of side 15.6 mm is 1.11 g/cm^3.
