1. **State the problem:** We need to find the density of a piece of metal given its mass and the change in water volume when it is submerged. 2. **Formula used:** Density is calculated by the formula $$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$ where volume is the volume of the metal. 3. **Calculate the volume of the metal:** $$\text{Volume} = 9.84\ \text{cm}^3 - 7.34\ \text{cm}^3 = 2.5\ \text{cm}^3$$ 4. **Calculate the density:** $$\text{Density} = \frac{28.3055\ \text{g}}{2.5\ \text{cm}^3}$$ 5. **Simplify the fraction:** $$\text{Density} = \frac{28.3055}{\cancel{2.5}} \times \frac{1}{\cancel{1}} = 11.3222\ \text{g/cm}^3$$ 6. **Final answer:** The density of the piece of metal is approximately **11.32 g/cm³**.