A sample of metal has a mass of 50.0 g and a volume of 20.0 cm^3. What would the density of another sample of the same metal be if its mass is 75.0 g and its volume is 30.0 cm^3?

• A. 0.4 g/cm^3
• B. 1.5 g/cm^3
• C. 3.0 g/cm^3
• D. 2.5 g/cm^3

Answer: (D)

Verified step by step guidance

1. Recall the formula for density, which is given by \(\text{density} = \frac{\text{mass}}{\text{volume}}\).
2. Calculate the density of the first metal sample using its mass and volume: \(\text{density}_1 = \frac{50.0\ \text{g}}{20.0\ \text{cm}^3}\).
3. Since the metal is the same, its density should be constant regardless of the sample size, so the density of the second sample should be the same as the first.
4. Calculate the density of the second sample using its mass and volume: \(\text{density}_2 = \frac{75.0\ \text{g}}{30.0\ \text{cm}^3}\).
5. Compare the calculated densities to confirm they are equal, which verifies the density of the second sample.