1. **State the problem:** We need to find the volume of a shape made from a hemisphere and a half-cylinder. The hemisphere has radius $r=5.3$ cm, and it sits on the half-cylinder whose base is a square with side length equal to the diameter of the hemisphere's base, i.e., $2r=10.6$ cm. 2. **Volume formulas:** - Volume of a sphere: $$V_{sphere} = \frac{4}{3}\pi r^3$$ - Volume of a hemisphere (half a sphere): $$V_{hemisphere} = \frac{1}{2} V_{sphere} = \frac{2}{3}\pi r^3$$ - Volume of a cylinder: $$V_{cylinder} = \pi r^2 h$$ 3. **Dimensions of the half-cylinder:** - The base is a square with side length $2r = 10.6$ cm. - The half-cylinder is formed by cutting a cylinder of radius $r=5.3$ cm in half along its length. - The height of the cylinder is the side length of the square base, so $h = 10.6$ cm. 4. **Calculate the volume of the hemisphere:** $$V_{hemisphere} = \frac{2}{3} \pi (5.3)^3 = \frac{2}{3} \pi (148.877) = 312.4 \text{ cm}^3 \text{ (approx)}$$ 5. **Calculate the volume of the full cylinder:** $$V_{cylinder} = \pi (5.3)^2 (10.6) = \pi (28.09)(10.6) = 936.3 \text{ cm}^3 \text{ (approx)}$$ 6. **Calculate the volume of the half-cylinder:** $$V_{half-cylinder} = \frac{1}{2} V_{cylinder} = \frac{1}{2} (936.3) = 468.15 \text{ cm}^3$$ 7. **Calculate the total volume of the shape:** $$V_{total} = V_{hemisphere} + V_{half-cylinder} = 312.4 + 468.15 = 780.55 \text{ cm}^3$$ 8. **Final answer rounded to 1 decimal place:** $$\boxed{780.6 \text{ cm}^3}$$