1. **Stating the problem:** We need to find the volume of a composite solid made of a cuboid and a pyramid placed on top of it. 2. **Given dimensions:** - Cuboid base: length = 20 cm, width = 20 cm, height = 32 cm - Pyramid height = 15 cm 3. **Formulas used:** - Volume of cuboid: $$V_{cuboid} = l \times w \times h$$ - Volume of pyramid: $$V_{pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ 4. **Calculate the volume of the cuboid:** $$V_{cuboid} = 20 \times 20 \times 32 = 12800 \text{ cm}^3$$ 5. **Calculate the base area of the pyramid:** Since the pyramid sits on top of the cuboid, its base area is the same as the cuboid's top face: $$\text{Base Area} = 20 \times 20 = 400 \text{ cm}^2$$ 6. **Calculate the volume of the pyramid:** $$V_{pyramid} = \frac{1}{3} \times 400 \times 15 = \frac{1}{3} \times 6000 = 2000 \text{ cm}^3$$ 7. **Calculate the total volume of the shape:** $$V_{total} = V_{cuboid} + V_{pyramid} = 12800 + 2000 = 14800 \text{ cm}^3$$ **Final answer:** The volume of the shape is **14800 cm³**.