1. **State the problem:** Calculate the volume of a solid consisting of a rectangular block with a square base of side length 6 cm and height 10 cm, topped by a right pyramid with the same square base and height 5 cm. 2. **Formulas used:** - Volume of rectangular block: $$V_{block} = \text{base area} \times \text{height}$$ - Volume of pyramid: $$V_{pyramid} = \frac{1}{3} \times \text{base area} \times \text{height}$$ 3. **Calculate base area:** Since the base is a square with side length 6 cm, $$\text{base area} = 6 \times 6 = 36 \text{ cm}^2$$ 4. **Calculate volume of the rectangular block:** $$V_{block} = 36 \times 10 = 360 \text{ cm}^3$$ 5. **Calculate volume of the pyramid:** $$V_{pyramid} = \frac{1}{3} \times 36 \times 5 = \frac{1}{3} \times 180 = 60 \text{ cm}^3$$ 6. **Calculate total volume of the solid:** $$V_{total} = V_{block} + V_{pyramid} = 360 + 60 = 420 \text{ cm}^3$$ **Final answer:** The volume of the solid is **420 cm³**.