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Let's work through the three questions one by one.

### **QUESTION 1**:
What is the volume of a piece of iron (density \( D = 7.9 \, \text{g/cm}^3 \)) that has a mass of 0.50 kg?

- **Formula to use**: 
  \[
  \text{Volume} = \frac{\text{Mass}}{\text{Density}}
  \]
  Ensure the mass is in grams (since density is in g/cm³).
  
  - Given:
    - Mass = 0.50 kg = 500 g (since \( 1 \, \text{kg} = 1000 \, \text{g} \))
    - Density \( D = 7.9 \, \text{g/cm}^3 \)

  \[
  \text{Volume} = \frac{500 \, \text{g}}{7.9 \, \text{g/cm}^3} \approx 63.29 \, \text{cm}^3
  \]
  So, the closest answer is **None of the above**.

---

### **QUESTION 2**:
A piece of platinum metal with a density of \( 21.5 \, \text{g/cm}^3 \) has a volume of \( 4.49 \, \text{cm}^3 \). What is the mass?

- **Formula to use**:
  \[
  \text{Mass} = \text{Density} \times \text{Volume}
  \]

  - Given:
    - Volume = \( 4.49 \, \text{cm}^3 \)
    - Density \( D = 21.5 \, \text{g/cm}^3 \)

  \[
  \text{Mass} = 21.5 \times 4.49 \approx 96.535 \, \text{g}
  \]
  The closest answer is **96.5 g**.

---

### **QUESTION 3**:
What is the density (in \( \text{g/cm}^3 \)) of a piece of metal that has a mass of 0.500 kg and a volume of 63 cm³?

- **Formula to use**:
  \[
  \text{Density} = \frac{\text{Mass}}{\text{Volume}}
  \]

  - Given:
    - Mass = 0.500 kg = 500 g
    - Volume = \( 63 \, \text{cm}^3 \)

  \[
  \text{Density} = \frac{500}{63} \approx 7.94 \, \text{g/cm}^3
  \]
  The correct answer is **7.94 g/cm³**.

---

Let me know if you'd like more details or clarifications!

### Expanding questions:
1. How would the result in Question 1 change if the mass was given in grams instead of kilograms?
2. What would be the volume of platinum in Question 2 if its mass was doubled?
3. In Question 3, how would the density change if the volume were halved but the mass stayed the same?
4. Can you explain how units conversion impacts calculations involving density?
5. How is density related to mass and volume on a molecular level?

### Tip:
Always check units (mass, volume, density) before performing calculations to avoid errors!

What is the volume of a piece of iron (D=7.9 g/cm³) that has a mass of 0.50kg?
A piece of platinum metal with a density of 21.5g/cm³ has a volume of 4.49cm³. What is the mass?
What is the density in g/cm³, of a piece of metal that has a mass of 500g and a volume of 63cm³?

This problem set involves calculating the volume, mass, and density of metals using given densities and mass values. Learn how to apply formulas such as Volume = Mass / Density and Mass = Density × Volume for metals like iron and platinum. Suitable for Grades 9-12.

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