1. **State the problem:** We need to find the amount of paper needed to cover the side of a cylindrical can. The can has a diameter of 10 cm and a height of 8 cm. 2. **Formula used:** The paper covers the lateral surface area of the cylinder, which is given by the formula: $$\text{Lateral Surface Area} = 2 \pi r h$$ where $r$ is the radius and $h$ is the height of the cylinder. 3. **Calculate the radius:** The diameter is 10 cm, so the radius is half of that: $$r = \frac{10}{2} = 5 \text{ cm}$$ 4. **Substitute values into the formula:** $$\text{Lateral Surface Area} = 2 \times 3.14 \times 5 \times 8$$ 5. **Calculate step-by-step:** $$2 \times 3.14 = 6.28$$ $$6.28 \times 5 = 31.4$$ $$31.4 \times 8 = 251.2$$ 6. **Final answer:** The amount of paper needed to cover the side of the can is: $$\boxed{251.2 \text{ cm}^2}$$