To determine which of the four substances the unknown sample is made of, we need to calculate its density and compare it with the given densities of aluminum, copper, iron, and titanium.
First, let's calculate the density of the unknown sample. Density is determined using the formula:
[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\][/tex]
For the unknown sample:
[tex]\[
\text{Mass} = 9.5 \, \text{g}
\][/tex]
[tex]\[
\text{Volume} = 21 \, \text{cm}^3
\][/tex]
So, the density of the unknown sample is:
[tex]\[
\text{Density}_{\text{unknown}} = \frac{9.5 \, \text{g}}{21 \, \text{cm}^3} \approx 0.45 \, \text{g/cm}^3
\][/tex]
Now, let's compare this density with the given densities of the four substances:
- Aluminum: [tex]\(2.7 \, \text{g/cm}^3\)[/tex]
- Copper: [tex]\(9.0 \, \text{g/cm}^3\)[/tex]
- Iron: [tex]\(7.9 \, \text{g/cm}^3\)[/tex]
- Titanium: [tex]\(4.8 \, \text{g/cm}^3\)[/tex]
The density of the unknown sample ([tex]\(\approx 0.45 \, \text{g/cm}^3\)[/tex]) is significantly lower than the densities of aluminum, copper, iron, and titanium. Thus, based on the given data, the unknown sample does not match the density of any of the four substances provided by Marcus. Therefore, the unknown sample is not made of any of the four substances listed in the table.
