1. **Problem 8:** Convert 8.2 cm on a map with scale 1:10,000 to actual distance in meters. 2. The scale 1:10,000 means 1 cm on the map represents 10,000 cm in reality. 3. To find the actual distance for 8.2 cm: $$\text{Actual distance} = 8.2 \times 10,000 = 82,000 \text{ cm}$$ 4. Convert cm to meters by dividing by 100: $$\frac{82,000}{100} = 820 \text{ meters}$$ 5. **Problem 9:** Find the map distance in cm for an actual distance of 3,000 meters with scale 1:10,000. 6. Convert 3,000 meters to cm: $$3,000 \times 100 = 300,000 \text{ cm}$$ 7. Using the scale 1:10,000, map distance is: $$\text{Map distance} = \frac{300,000}{10,000} = 30 \text{ cm}$$ **Final answers:** - Problem 8: Actual distance = 820 meters - Problem 9: Map distance = 30 cm