Given the scale of 1 : 60,000, this means that 1 unit on the map represents 60,000 units in reality. To find the actual distance, you multiply the scaled distance by 60,000.

a) 9 cm on the map

$\text{Actual distance} = 9 \, \text{cm} \times 60,000 = 540,000 \, \text{cm}$ Now, convert centimeters to kilometers (since 100,000 cm = 1 km): $540,000 \, \text{cm} = \frac{540,000}{100,000} = 5.4 \, \text{km}$ So, the actual distance is 5.4 km.

b) 8 mm on the map

First, convert 8 mm to cm (since 1 cm = 10 mm): $8 \, \text{mm} = 0.8 \, \text{cm}$ Now, calculate the actual distance: $\text{Actual distance} = 0.8 \, \text{cm} \times 60,000 = 48,000 \, \text{cm}$ Convert centimeters to kilometers: $48,000 \, \text{cm} = \frac{48,000}{100,000} = 0.48 \, \text{km}$ So, the actual distance is 0.48 km.

Would you like more details on these calculations or have any other questions?

Here are 5 related questions for further exploration:

1. How would the actual distance change if the scale was 1 : 100,000?
2. How can you convert an actual distance back to the map distance using the scale?
3. What would be the actual distance if the scaled distance was 12 cm on the same map?
4. How does the scale of the map affect the level of detail shown?
5. How can you estimate distances on a map if you know the scale but don't have a ruler?

Tip: Always convert all measurements to the same units before performing calculations for accuracy.