You have a 100 gram sample of each of the following metals. Which sample has the largest volume?

• A. Gold (density = 19.3 g/cm^3)
• B. Aluminum (density = 2.70 g/cm^3)
• C. Iron (density = 7.87 g/cm^3)
• D. Copper (density = 8.96 g/cm^3)

Answer: (B)

Verified step by step guidance

1. Recall the relationship between mass, volume, and density, which is given by the formula: \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\).
2. Rearrange the formula to solve for volume: \(\text{Volume} = \frac{\text{Mass}}{\text{Density}}\).
3. Since each metal sample has the same mass (100 grams), calculate the volume of each metal by dividing 100 grams by its respective density: \(V = \frac{100\ \text{g}}{\text{density}}\).
4. Compare the calculated volumes for gold, aluminum, iron, and copper. The metal with the smallest density will have the largest volume because volume is inversely proportional to density when mass is constant.
5. Identify aluminum as the metal with the lowest density (2.70 g/cm\(^{3}\)), which means it will have the largest volume among the given samples.