In order to determine which city has the largest number of people in the smallest amount of space, we need to calculate the area (in square miles) for each city. To find the area, we will use the formula:
[tex]\[
\text{Area} = \frac{\text{Population}}{\text{Population Density}}
\][/tex]
Let's proceed with the calculations for each city:
### Delhi (India)
[tex]\[
\text{Population Density} = 30,400 \, \text{people per sq mi}
\][/tex]
[tex]\[
\text{Population} = 22,826,000 \, \text{people}
\][/tex]
[tex]\[
\text{Area} = \frac{22,826,000}{30,400} \approx 750.86 \, \text{sq mi}
\][/tex]
### Manila (Philippines)
[tex]\[
\text{Population Density} = 38,300 \, \text{people per sq mi}
\][/tex]
[tex]\[
\text{Population} = 21,241,000 \, \text{people}
\][/tex]
[tex]\[
\text{Area} = \frac{21,241,000}{38,300} \approx 554.60 \, \text{sq mi}
\][/tex]
### Karachi (Pakistan)
[tex]\[
\text{Population Density} = 67,300 \, \text{people per sq mi}
\][/tex]
[tex]\[
\text{Population} = 20,877,000 \, \text{people}
\][/tex]
[tex]\[
\text{Area} = \frac{20,877,000}{67,300} \approx 310.21 \, \text{sq mi}
\][/tex]
### New York (US)
[tex]\[
\text{Population Density} = 4,600 \, \text{people per sq mi}
\][/tex]
[tex]\[
\text{Population} = 20,673,000 \, \text{people}
\][/tex]
[tex]\[
\text{Area} = \frac{20,673,000}{4,600} \approx 4494.13 \, \text{sq mi}
\][/tex]
Now we compare these 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, we can see that Karachi has the smallest area. Therefore, Karachi has the largest number of people in the smallest amount of space.
The city with the largest number of people in the smallest amount of space is Karachi.
