1. **Problem statement:** A cylindrical block of metal with diameter 1 m and height 2 m is melted to form 2000 cubes. Find the length of each side of the cube in cm. 2. **Formula and rules:** - Volume of cylinder: $$V = \pi r^2 h$$ where $r$ is radius and $h$ is height. - Volume of one cube: $$s^3$$ where $s$ is the side length. - Total volume of cubes equals volume of cylinder. - Convert all units consistently (1 m = 100 cm). 3. **Calculate volume of cylinder:** - Radius $r = \frac{1}{2} = 0.5$ m - Height $h = 2$ m - Volume $$V = \pi (0.5)^2 \times 2 = \pi \times 0.25 \times 2 = 0.5\pi \text{ m}^3$$ 4. **Convert volume to cm³:** - $1 \text{ m}^3 = 100^3 = 1,000,000 \text{ cm}^3$ - So, $$V = 0.5\pi \times 1,000,000 = 500,000\pi \text{ cm}^3$$ 5. **Volume of one cube:** - Total volume divided by number of cubes: $$s^3 = \frac{500,000\pi}{2000} = 250\pi \text{ cm}^3$$ 6. **Find side length $s$:** $$s = \sqrt[3]{250\pi}$$ 7. **Calculate numerical value:** - Approximate $\pi \approx 3.1416$ - $$s = \sqrt[3]{250 \times 3.1416} = \sqrt[3]{785.4}$$ - Cube root of 785.4 is approximately 9.24 cm **Final answer:** The length of each side of the cube is approximately **9.24 cm**.