To determine which state has the greatest population density, we need to calculate the population density for each state. Population density is calculated by dividing the population of the state by its area (in square miles). Here is a detailed, step-by-step solution:
### Step 1: List the Populations and Areas
The given populations are:
- North Dakota: 780,000
- South Dakota: 887,000
- Nebraska: 1,960,000
- Kansas: 2,940,000
The given approximate areas in square miles are:
- North Dakota: 70,700
- South Dakota: 77,116
- Nebraska: 77,354
- Kansas: 82,278
### Step 2: Calculate Population Density
To calculate the population density, use the formula:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} \][/tex]
Let's calculate the population density for each state:
#### North Dakota:
[tex]\[ \text{Population Density}_{\text{ND}} = \frac{780,000}{70,700} \approx 11.03 \, \text{people/sq. mile} \][/tex]
#### South Dakota:
[tex]\[ \text{Population Density}_{\text{SD}} = \frac{887,000}{77,116} \approx 11.50 \, \text{people/sq. mile} \][/tex]
#### Nebraska:
[tex]\[ \text{Population Density}_{\text{NE}} = \frac{1,960,000}{77,354} \approx 25.34 \, \text{people/sq. mile} \][/tex]
#### Kansas:
[tex]\[ \text{Population Density}_{\text{KS}} = \frac{2,940,000}{82,278} \approx 35.73 \, \text{people/sq. mile} \][/tex]
### Step 3: Compare the Population Densities
Now that we have the population densities for each state:
- North Dakota: \( 11.03 \, \text{people/sq. mile} \)
- South Dakota: \( 11.50 \, \text{people/sq. mile} \)
- Nebraska: \( 25.34 \, \text{people/sq. mile} \)
- Kansas: \( 35.73 \, \text{people/sq. mile} \)
### Conclusion
By comparing the population densities, we see that Kansas has the greatest population density of \( 35.73 \, \text{people/sq. mile} \).
Therefore, the state with the greatest population density is:
B. Kansas
