To determine which sample has the largest volume, we need to calculate the volume of each metal sample using the formula for density:

Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass​Rearranging the formula to solve for volume:

Volume=MassDensity\text{Volume} = \frac{\text{Mass}}{\text{Density}}Volume=DensityMass​Given that the mass of each sample is 100 grams, we can calculate the volume for each metal:

1. Aluminum (d = 2.7 g/cm³):

Volume=100 g2.7 g/cm3≈37.04 cm3\text{Volume} = \frac{100 \, \text{g}}{2.7 \, \text{g/cm}^3} \approx 37.04 \, \text{cm}^3Volume=2.7g/cm3100g​≈37.04cm3

2. Gold (d = 19.3 g/cm³):

Volume=100 g19.3 g/cm3≈5.18 cm3\text{Volume} = \frac{100 \, \text{g}}{19.3 \, \text{g/cm}^3} \approx 5.18 \, \text{cm}^3Volume=19.3g/cm3100g​≈5.18cm3

3. Iron (d = 7.86 g/cm³):

Volume=100 g7.86 g/cm3≈12.73 cm3\text{Volume} = \frac{100 \, \text{g}}{7.86 \, \text{g/cm}^3} \approx 12.73 \, \text{cm}^3Volume=7.86g/cm3100g​≈12.73cm3

4. Magnesium (d = 1.74 g/cm³):

Volume=100 g1.74 g/cm3≈57.47 cm3\text{Volume} = \frac{100 \, \text{g}}{1.74 \, \text{g/cm}^3} \approx 57.47 \, \text{cm}^3Volume=1.74g/cm3100g​≈57.47cm3

5. Silver (d = 10.5 g/cm³):

Volume=100 g10.5 g/cm3≈9.52 cm3\text{Volume} = \frac{100 \, \text{g}}{10.5 \, \text{g/cm}^3} \approx 9.52 \, \text{cm}^3Volume=10.5g/cm3100g​≈9.52cm3The metal with the largest volume is magnesium, with a volume of approximately 57.47 cm³. This is because magnesium has the lowest density (1.74 g/cm³) among the given metals.