To identify which metal has the lowest density, we need to calculate the density of each metal using their given volumes and masses. Density is calculated as \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\).
Let's go through the calculations step-by-step for each metal:
1. Metal A:
- Volume: \(12.5 \; cm^3\)
- Mass: \(122 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{122 \; g}{12.5 \; cm^3} = 9.76 \; g/cm^3\)
2. Metal B:
- Volume: \(14.2 \; cm^3\)
- Mass: \(132 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{132 \; g}{14.2 \; cm^3} \approx 9.30 \; g/cm^3\)
3. Metal C:
- Volume: \(18.1 \; cm^3\)
- Mass: \(129 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{129 \; g}{18.1 \; cm^3} \approx 7.13 \; g/cm^3\)
4. Metal D:
- Volume: \(12.7 \; cm^3\)
- Mass: \(126 \; g\)
- Density\( = \frac{Mass}{Volume} = \frac{126 \; g}{12.7 \; cm^3} \approx 9.92 \; g/cm^3\)
Now we have the densities of all metals:
- Metal A: \(9.76 \; g/cm^3\)
- Metal B: \(9.30 \; g/cm^3\)
- Metal C: \(7.13 \; g/cm^3\)
- Metal D: \(9.92 \; g/cm^3\)
From these calculations, we can see that the metal with the lowest density is Metal C, which has a density of approximately \(7.13 \; g/cm^3\).
Therefore, the unidentified metal with the lowest density is Metal C.
