Answer: There are 640 acres in a square mile.
An acre is a unit of land area commonly used in the United States, equivalent to 43,560 square feet, and a square mile is an imperial unit representing an area of 640 acres or 2.59 square kilometers. Let's understand the relationship between Acres and Square Miles.
One acre is defined as 43,560 square feet. A square mile, as the name suggests, is the area of a square with each side measuring one mile in length. Since one mile is equal to 5,280 feet, a square mile is a square with each side of 5,280 feet.
The area of a square is calculated by squaring the length of its side, so the area of a square mile is:
5,280 feet × 5,280 feet = 27,878,400 square feet
To find out how many acres are in a square mile, we divide the total square feet in a square mile by the square feet in an acre:
27,878,400 square feet ÷ 43,560 square feet per acre=640 acres
Therefore, there are 640 acres in a square mile.
Practice Problems
Question 1: A rectangular field measures 1/2 mile by 3/4 mile. How many acres does it cover?
Question 2: A square plot of land contains 2560 acres. What is the length of one side in miles?
Question 3: A triangular field has a base of 880 yards and a height of 660 yards. How many acres is it?
Question 4: A farmer owns a square plot of land that is 1/4 mile on each side. He wants to fence it with a 4-strand barbed wire fence. How many feet of barbed wire does he need?
Question 5: A developer wants to subdivide a 640-acre tract into 1-acre lots. How many lots can be created?
Question 6: A forest ranger estimates that a fire has burned through 5 square miles of forest. How many acres is this?
Question 7: A property tax is assessed at $2.50 per acre. How much tax is owed on a rectangular property that is 1/2 mile by 1/4 mile?
Question 8: A farmer harvests 150 bushels of corn per acre. How many bushels are harvested from a square field with side length 1/2 mile?
Question 9: A developer wants to create a housing subdivision on a 100-acre tract. Each house lot will be 1/4 acre, and 20% of the land will be dedicated to green space. How many house lots can be created?
Question 10: A circular area has a radius of 1 mile. What is its approximate area in acres?