1. **State the problem:** We need to find the mass of a gold bar with given dimensions and density. The dimensions are 10 inches long, 3 inches wide, and 1.5 inches high. The density of gold is 19.32 g/cm³. We want the mass in kilograms, rounded to two decimal places. 2. **Convert dimensions to centimeters:** Since 1 inch = 2.54 cm, $$\text{length} = 10 \times 2.54 = 25.4 \, \text{cm}$$ $$\text{width} = 3 \times 2.54 = 7.62 \, \text{cm}$$ $$\text{height} = 1.5 \times 2.54 = 3.81 \, \text{cm}$$ 3. **Calculate the volume of the gold bar:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height} = 25.4 \times 7.62 \times 3.81$$ $$= 737.146 \text{ cm}^3$$ 4. **Calculate the mass in grams using density:** $$\text{Mass} = \text{Density} \times \text{Volume} = 19.32 \times 737.146 = 14238.5 \text{ g}$$ 5. **Convert mass to kilograms:** Since 1000 g = 1 kg, $$\text{Mass} = \frac{14238.5}{1000} = 14.2385 \text{ kg}$$ 6. **Round the mass to two decimal places:** $$\boxed{14.24 \text{ kg}}$$ **Final answer:** The mass of the gold bar is approximately **14.24 kg**.