1. **State the problem:** We have a sculpture made of two parts: a cuboid and a square-based pyramid on top. Both have bases of side 3 cm. 2. **Given data:** - Side of base (cuboid and pyramid): $3$ cm - Height of cuboid: $8$ cm - Total height of sculpture: $15$ cm - Total mass of sculpture: $738$ g - Density of iron (cuboid): $7.8$ g/cm$^3$ - Density of copper (pyramid): unknown, to be found 3. **Calculate the height of the pyramid:** $$\text{Height of pyramid} = 15 - 8 = 7 \text{ cm}$$ 4. **Calculate the volume of the cuboid:** $$\text{Volume}_{cuboid} = \text{base area} \times \text{height} = 3 \times 3 \times 8 = 72 \text{ cm}^3$$ 5. **Calculate the volume of the pyramid:** $$\text{Volume}_{pyramid} = \frac{1}{3} \times \text{base area} \times \text{height} = \frac{1}{3} \times 3 \times 3 \times 7 = \frac{1}{3} \times 9 \times 7 = 21 \text{ cm}^3$$ 6. **Calculate the mass of the cuboid:** $$\text{Mass}_{cuboid} = \text{density} \times \text{volume} = 7.8 \times 72 = 561.6 \text{ g}$$ 7. **Calculate the mass of the pyramid:** $$\text{Mass}_{pyramid} = \text{total mass} - \text{mass}_{cuboid} = 738 - 561.6 = 176.4 \text{ g}$$ 8. **Calculate the density of copper (pyramid):** $$\text{Density}_{copper} = \frac{\text{mass}_{pyramid}}{\text{volume}_{pyramid}} = \frac{176.4}{21} = 8.4 \text{ g/cm}^3$$ **Final answer:** The density of the copper is $8.4$ g/cm$^3$.