3. Calculate the density of the metal bar in g/cm³.

ANSWER:

WORKED OUT SOLUTION:

We are asked to calculate the density of the metal. We are given a mass of 156.4 g. The volume can be calculated from the length, width, and thickness of the metal bar. We are asked to calculate the density in g/cm³.

\(\displaystyle Volume\;=\;length\times{width}\times{thickness}\)
 
First, we convert the length, width, and the thickness from inches to cm and then we can calculate the volume.
 
\(\displaystyle\require{cancel}0.772\;\cancel{in}\times\frac{2.54\;cm}{1\;\cancel{in}}\;=\;\mathbf{1.9\underline{6}088\;cm}\)
 
\(\displaystyle 0.221\;\cancel{in}\times\frac{2.54\;cm}{1\;\cancel{in}}\;=\;\mathbf{0.56\underline{1}34\;cm}\)
 
\(\displaystyle 2.61\;\cancel{in}\times\frac{2.54\;cm}{1\;\cancel{in}}\;=\;\mathbf{6.6\underline{2}94\;cm}\)
 

Next, we calculate the volume.

\(V\;=\;1.9\underline{6}088\;cm\times{0.56\underline{1}34\;cm}\times{6.6\underline{2}94\;cm}\;=\;\mathbf{7.2\underline{9}71\;cm^3}\)
 
Now, we are ready to calculate the density.
 
\(\displaystyle\; d\;=\;\frac{m}{V}\;=\;\frac{156.4\;g}{7.2\underline{9}71\;cm^3}\;=\;\mathbf{21.4\;g/cm^3}\)
 

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