To determine which city has the largest number of people in the smallest amount of space, we need to calculate the area of each city based on its population and population density. The formula for area is:
[tex]\[ \text{Area} = \frac{\text{Population}}{\text{Population Density}} \][/tex]
Let's calculate the area for each city:
1. Delhi (India)
- Population: 22,826,000
- Population Density: 30,400 people per square mile
- Area:
[tex]\[
\frac{22,826,000}{30,400} \approx 750.86 \, \text{sq mi}
\][/tex]
2. Manila (Philippines)
- Population: 21,241,000
- Population Density: 38,300 people per square mile
- Area:
[tex]\[
\frac{21,241,000}{38,300} \approx 554.60 \, \text{sq mi}
\][/tex]
3. Karachi (Pakistan)
- Population: 20,877,000
- Population Density: 67,300 people per square mile
- Area:
[tex]\[
\frac{20,877,000}{67,300} \approx 310.21 \, \text{sq mi}
\][/tex]
4. New York (US)
- Population: 20,673,000
- Population Density: 4,600 people per square mile
- Area:
[tex]\[
\frac{20,673,000}{4,600} \approx 4494.13 \, \text{sq mi}
\][/tex]
Now, let's compare the calculated areas:
- Delhi: 750.86 sq mi
- Manila: 554.60 sq mi
- Karachi: 310.21 sq mi
- New York: 4494.13 sq mi
From the calculations, Karachi has the smallest area with approximately 310.21 square miles. Therefore, Karachi is the city with the largest number of people in the smallest amount of space.
