Question
Three different maps of the same region at different scales. Scale of Figure 4 a is 1 to 24,000, 1 inch = 2000 feet. Area shown is 1 square mile. Figure 4 b is 1 to 62,500. 1 inch = nearly 1 mile. Area shown is 6 and three-quarters scale miles. Figure 4 c is 1 to 250,000. 1 inch = nearly 4 miles. Area shown is 107 square miles.
Using scale, which map shows the most area per inch?
a.
4a
c.
4c
b.
4b
d.
they are the same
Please select the best answer from the choices provided
A
B
C
D
Answers
GPT-4o mini
To determine which map shows the most area per inch, we need to analyze the scales and areas shown for each map.
1. **Figure 4a**:
- Scale: 1:24,000 (1 inch = 2,000 feet)
- Area shown: 1 square mile
- To find the area per inch, we convert square miles to square inches (understanding that there are 640 acres in a square mile and 43,560 square feet in an acre):
- 1 square mile = 640 acres = 27,878,400 square feet
- Therefore, the area per inch = \( \frac{27,878,400 \text{ square feet}}{2,000 \text{ feet}} = 13,939.2\) square feet per inch.
2. **Figure 4b**:
- Scale: 1:62,500 (1 inch ≈ 1 mile)
- Area shown: 6.75 scale miles
- 1 square mile = 27,878,400 square feet, so:
- 6.75 square miles = \( 6.75 \times 27,878,400 \text{ square feet} = 188,368,800\text{ square feet}\)
- Therefore, the area per inch is about \( \frac{188,368,800 \text{ square feet}}{5,280 \text{ feet}} = 35,668.5\) square feet per inch.
3. **Figure 4c**:
- Scale: 1:250,000 (1 inch ≈ 4 miles)
- Area shown: 107 square miles
- 107 square miles = \( 107 \times 27,878,400 \text{ square feet} = 2,978,483,200\text{ square feet}\)
- Therefore, the area per inch is about \( \frac{2,978,483,200 \text{ square feet}}{21,120 \text{ feet}} = 141,932.29\) square feet per inch.
By comparing areas per inch:
- Figure 4a: 13,939.2 square feet/inch
- Figure 4b: 35,668.5 square feet/inch
- Figure 4c: 141,932.29 square feet/inch
The largest area per inch is from **Figure 4c**.
Thus, the answer is:
**C. 4c**.
1. **Figure 4a**:
- Scale: 1:24,000 (1 inch = 2,000 feet)
- Area shown: 1 square mile
- To find the area per inch, we convert square miles to square inches (understanding that there are 640 acres in a square mile and 43,560 square feet in an acre):
- 1 square mile = 640 acres = 27,878,400 square feet
- Therefore, the area per inch = \( \frac{27,878,400 \text{ square feet}}{2,000 \text{ feet}} = 13,939.2\) square feet per inch.
2. **Figure 4b**:
- Scale: 1:62,500 (1 inch ≈ 1 mile)
- Area shown: 6.75 scale miles
- 1 square mile = 27,878,400 square feet, so:
- 6.75 square miles = \( 6.75 \times 27,878,400 \text{ square feet} = 188,368,800\text{ square feet}\)
- Therefore, the area per inch is about \( \frac{188,368,800 \text{ square feet}}{5,280 \text{ feet}} = 35,668.5\) square feet per inch.
3. **Figure 4c**:
- Scale: 1:250,000 (1 inch ≈ 4 miles)
- Area shown: 107 square miles
- 107 square miles = \( 107 \times 27,878,400 \text{ square feet} = 2,978,483,200\text{ square feet}\)
- Therefore, the area per inch is about \( \frac{2,978,483,200 \text{ square feet}}{21,120 \text{ feet}} = 141,932.29\) square feet per inch.
By comparing areas per inch:
- Figure 4a: 13,939.2 square feet/inch
- Figure 4b: 35,668.5 square feet/inch
- Figure 4c: 141,932.29 square feet/inch
The largest area per inch is from **Figure 4c**.
Thus, the answer is:
**C. 4c**.