To identify the unknown sample, we need to calculate its density using the given mass and volume, and then compare this density to those of the known substances: aluminum, copper, iron, and titanium.
Step 1: Calculate the density of the unknown sample.
Given:
- Mass of the unknown sample = 9.5 grams
- Volume of the unknown sample = 2.1 cubic centimeters
Density is calculated using the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Substituting the given values:
[tex]\[ \text{Density of the unknown sample} = \frac{9.5 \, \text{g}}{2.1 \, \text{cm}^3} \][/tex]
[tex]\[
\text{Density of the unknown sample} = 4.523809523809524 \, \text{g/cm}^3
\][/tex]
Step 2: Compare the calculated density of the unknown sample with the densities of the known substances.
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Substance} & \text{Density} (\text{g/cm}^3) \\
\hline
\text{aluminum} & 2.7 \\
\hline
\text{copper} & 9.0 \\
\hline
\text{iron} & 7.9 \\
\hline
\text{titanium} & 4.8 \\
\hline
\end{array}
\][/tex]
Step 3: Determine which known substance has a density that closely matches the calculated density of the unknown sample.
The calculated density of 4.523809523809524 g/cm³ (rounding to one decimal place: approximately 4.5) does not exactly match any of the given densities in the table. The closest density is that of titanium, which is 4.8 g/cm³, but it is not an exact match.
As there is no exact match in the provided densities, the closest match would still not be accurate.
Therefore, the unknown sample does not precisely match any of the densities of aluminum, copper, iron, or titanium provided in the table.
The unknown sample must be made of an unknown substance not listed in Marcus's original measurements.
Hence, the correct answer is:
[tex]\[
\boxed{\text{Unknown Substance}}
\][/tex]
