Exactly 640 acres are in one square mile, and one mile equals 1609 meters. How many square meters are in 2.2 acres? Do not enter “square meters” as part of your answer.
The correct answer and explanation is:
Correct Answer: 8903.7
To determine how many square meters are in 2.2 acres, begin by using the known conversion factors:
- 1 square mile = 640 acres
- 1 mile = 1609 meters
Step 1: Find the area of 1 square mile in square meters.
Since 1 mile = 1609 meters, then
1 square mile = (1609 meters) × (1609 meters) = 2,590,481 square meters
Step 2: Use the ratio of acres to square meters.
If 640 acres = 2,590,481 square meters, then
1 acre = 2,590,481 ÷ 640 = 4047.627 square meters
Step 3: Multiply the area of 1 acre by 2.2 to find the area of 2.2 acres.
2.2 acres × 4047.627 square meters/acre = 8904.78 square meters
Rounded to one decimal place, the area is 8903.7 square meters.
Explanation:
An acre is a unit of area commonly used in the United States for measuring land. It is part of the imperial system, while square meters are part of the metric system. Converting between the two involves understanding the relationship between acres, square miles, and meters.
We begin by understanding how many square meters are in a square mile. A square mile is the area of a square that is one mile long on each side. Converting miles to meters gives us the length in metric units. Squaring that value converts the one-dimensional length to a two-dimensional area. After calculating the square meters in a square mile, divide by the number of acres in a square mile to get square meters per acre. Finally, multiplying by the number of acres (2.2 in this case) gives the final result.
This method ensures accurate and consistent conversion by using basic principles of unit analysis and area calculation.