1. **Problem 1:** Find the area occupied on a plan drawn to a scale of 1 : 500 by the Olympic Stadium in Beijing, which is $\frac{3}{5}$ of 8 (units not specified, assume 8 square units). 2. **Step 1:** Understand the scale. A scale of 1 : 500 means 1 unit on the plan represents 500 units in reality. 3. **Step 2:** Calculate the actual area of the stadium. $$\text{Actual area} = \frac{3}{5} \times 8 = \frac{24}{5} = 4.8$$ 4. **Step 3:** To find the area on the plan, we use the scale factor for area, which is the square of the linear scale factor. $$\text{Scale factor for area} = \left(\frac{1}{500}\right)^2 = \frac{1}{250000}$$ 5. **Step 4:** Calculate the area on the plan. $$\text{Area on plan} = \text{Actual area} \times \text{Scale factor for area} = 4.8 \times \frac{1}{250000} = \frac{4.8}{250000} = 0.0000192$$ 6. **Answer for Problem 1:** The area occupied on the plan is $0.0000192$ square units. --- 7. **Problem 2:** On a map of scale 1 : 20 000, the area of a forest is 50 cm². On another map, the area is 8 cm². Find the scale of the second map. 8. **Step 1:** Let the scale of the second map be 1 : $x$. 9. **Step 2:** The actual area of the forest is the same, so calculate it from the first map. $$\text{Actual area} = \text{Map area} \times (\text{Scale factor})^2 = 50 \times (20000)^2 = 50 \times 400000000 = 20000000000$$ 10. **Step 3:** Using the second map's area, set up the equation: $$8 \times x^2 = 20000000000$$ 11. **Step 4:** Solve for $x^2$: $$x^2 = \frac{20000000000}{8} = 2500000000$$ 12. **Step 5:** Find $x$: $$x = \sqrt{2500000000} = 50000$$ 13. **Answer for Problem 2:** The scale of the second map is 1 : 50000. --- **Final answers:** - Area on plan for Olympic Stadium: $0.0000192$ square units. - Scale of second map: 1 : 50000.