1. **Stating the problem:** A cylindrical block of metal with diameter 1 m and height 2 m is melted to form 2000 cubes. We need to find the length of each side of the cube in cm. 2. **Formula for volume of cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the volume of the cylinder:** Diameter = 1 m, so radius $r = \frac{1}{2} = 0.5$ m. Height $h = 2$ m. $$V = \pi \times (0.5)^2 \times 2 = \pi \times 0.25 \times 2 = 0.5\pi \text{ cubic meters}$$ 4. **Convert volume to cubic centimeters:** Since 1 m = 100 cm, 1 cubic meter = $100^3 = 1,000,000$ cubic cm. $$V = 0.5\pi \times 1,000,000 = 500,000\pi \text{ cubic cm}$$ 5. **Volume of one cube:** Total volume is divided into 2000 cubes, so volume of one cube: $$V_{cube} = \frac{500,000\pi}{2000} = 250\pi \text{ cubic cm}$$ 6. **Find the side length of the cube:** Volume of cube = side$^3$, so $$s^3 = 250\pi$$ $$s = \sqrt[3]{250\pi}$$ 7. **Calculate the numerical value:** Using $\pi \approx 3.1416$, $$s = \sqrt[3]{250 \times 3.1416} = \sqrt[3]{785.4} \approx 9.24 \text{ cm}$$ **Final answer:** The length of each side of the cube is approximately **9.24 cm**.