A square mile is an area of land measuring one mile on each side. If you multiply that by the number of miles around a sphere, you get the total surface area of the sphere. On a flat plane, this number would be 3.14 times as great because a plane is not curved like a sphere is. On a sphere, this number would be four times as great.
As far as I can determine, there are 5280 feet in one mile. That means that you could fit 41960 square feet into one square mile or roughly 420160 square feet to account for the curvature of the earth. If you multiply 420160 times 4 (for the curvature of a sphere) and divide by 5280, you get 10498840 square feet per mile or roughly 104 acres per mile.