1. **State the problem:** We need to find the volume of a 3D shape whose cross-section is made up of a rectangle and two semicircles at its ends. The rectangle has length 10 cm and height 5 cm. The two semicircles have a combined diameter of 8 cm, so each semicircle has radius 4 cm. 2. **Calculate the area of the rectangular part of the cross-section:** $$\text{Area}_{rectangle} = \text{length} \times \text{height} = 10 \times 5 = 50 \text{ cm}^2$$ 3. **Calculate the area of the two semicircles combined:** Two semicircles make a full circle. $$\text{Radius } r = 4 \text{ cm}$$ $$\text{Area}_{circle} = \pi r^2 = \pi \times 4^2 = 16\pi \text{ cm}^2$$ 4. **Calculate total cross-sectional area:** $$\text{Area}_{total} = \text{Area}_{rectangle} + \text{Area}_{circle} = 50 + 16\pi$$ 5. **Calculate the volume of the shape:** The length of the shape in the direction perpendicular to the cross-section is 10 cm. $$\text{Volume} = \text{Area}_{total} \times \text{length} = (50 + 16\pi) \times 10 = 500 + 160\pi \text{ cm}^3$$ 6. **Get the numerical value and round to 3 significant figures:** Use $$\pi \approx 3.142$$ $$\text{Volume} \approx 500 + 160 \times 3.142 = 500 + 502.72 = 1002.72 \text{ cm}^3$$ Rounding to 3 s.f.: $$\boxed{1000 \text{ cm}^3}$$