Question
If you know that the town of Paarl has a population of approximately 125 250 people, and you know that each square is 9 cm by 10 cm on a 1: 50 000 topographical map, how many people live in each square kilometre on average? Your answer should be rounded off to the nearest number
Answers
GPT-4o mini
To calculate the number of people living in each square kilometer, we can follow these steps:
1. **Determine the area represented by one square on the map**:
- Each square measures 9 cm by 10 cm.
- Area in square centimeters = \(9 \, \text{cm} \times 10 \, \text{cm} = 90 \, \text{cm}^2\).
2. **Convert the area on the map to real-world area**:
- The scale is 1:50,000, meaning 1 cm on the map represents 50,000 cm in reality.
- Converting cm to km: \(50,000 \, \text{cm} = 0.5 \, \text{km}\).
- Therefore, the area in km² represented by one square on the map is:
\[
\text{Area} = 0.5 \, \text{km} \times 0.5 \, \text{km} = 0.25 \, \text{km}^2.
\]
3. **Calculate the average population density**:
- The population of Paarl is approximately 125,250 people.
- To find the population density:
\[
\text{Population Density} = \frac{\text{Population}}{\text{Total Area in km}^2} = \frac{125,250 \, \text{people}}{125 \, \text{km}^2} = 1,002.
\]
4. **Determine the number of people per square kilometer**:
- Since 1 square on the map corresponds to 0.25 km², the population per km² is:
\[
\text{Population in } 0.25 \, \text{km}^2 = \frac{125,250}{0.25} = 501,000 \text{ people/km}^2.
\]
Thus, the average number of people living in each square kilometer, rounded to the nearest number, is approximately **501,000** people/km².
1. **Determine the area represented by one square on the map**:
- Each square measures 9 cm by 10 cm.
- Area in square centimeters = \(9 \, \text{cm} \times 10 \, \text{cm} = 90 \, \text{cm}^2\).
2. **Convert the area on the map to real-world area**:
- The scale is 1:50,000, meaning 1 cm on the map represents 50,000 cm in reality.
- Converting cm to km: \(50,000 \, \text{cm} = 0.5 \, \text{km}\).
- Therefore, the area in km² represented by one square on the map is:
\[
\text{Area} = 0.5 \, \text{km} \times 0.5 \, \text{km} = 0.25 \, \text{km}^2.
\]
3. **Calculate the average population density**:
- The population of Paarl is approximately 125,250 people.
- To find the population density:
\[
\text{Population Density} = \frac{\text{Population}}{\text{Total Area in km}^2} = \frac{125,250 \, \text{people}}{125 \, \text{km}^2} = 1,002.
\]
4. **Determine the number of people per square kilometer**:
- Since 1 square on the map corresponds to 0.25 km², the population per km² is:
\[
\text{Population in } 0.25 \, \text{km}^2 = \frac{125,250}{0.25} = 501,000 \text{ people/km}^2.
\]
Thus, the average number of people living in each square kilometer, rounded to the nearest number, is approximately **501,000** people/km².