Question

A small cube of aluminum measures 15.6 mm on each side and weighs 4.20g. What is the density of aluminum in g/cm3?

Answer 1

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:

`\text{Volume of a cube=a}\cdot a\cdot a=a^3.`

Where a is the value of side, in this case, is 15.6 mm:

`\text{Volume}=15.6mm\cdot15.6mm\cdot15.6mm=15.6^3mm^3=3796.416mm^3.`

Now, let's convert the volume from mm^3 to cm^3. Remember that 1 cm^3 equals 1000 mm^3:

`3796.416mm^3\cdot(1cm^3)/(1000mm^3)=3.796cm^3\approx3.80cm^3.`

And we can replace the data that we have in the formula of density:

`\begin{gathered} \text{density}=(mass)/(volume), \\ \text{density}=\frac{4.20\text{ g}}{3.80cm^3}, \\ \text{density}=1.105\text{ }(g)/(cm^3)\approx1.11(g)/(cm^3). \end{gathered}`

The answer is that the density of the cube of aluminum of side 15.6 mm is 1.11 g/cm^3.