By calculating the density of the unknown metal sample and comparing it with the known metal samples, it is inferred that the unknown sample is likely to be lead (Option C: lead 11.34).
To identify the unknown metal sample, we can calculate its density and compare it with the densities of the known metal samples. The density is given by the formula: density = mass / volume.
For the unknown sample:
Density = 33.5 g / 3.2 cm^3 ≈ 10.47 g/cm^3.
Now, we compare this density with the densities of the known metal samples:
Aluminum: 14.6 g / 5.4 cm^3 ≈ 2.70 g/cm^3.
Iron: 33.1 g / 4.2 cm^3 ≈ 7.87 g/cm^3.
Lead: 35.2 g / 3.1 cm^3 ≈ 11.34 g/cm^3.
Magnesium: 10.6 g / 6.1 cm^3 ≈ 1.74 g/cm^3.
Silver: 47.2 g / 4.5 cm^3 ≈ 10.49 g/cm^3.
Comparing the calculated density of the unknown sample (10.47 g/cm³) with the densities of the known samples, it is closest to the density of lead (11.34 g/cm³). Therefore, the unknown sample is likely to be lead.