# If I built a circular fence that was 4.5 miles long, how many acres of land would it contain?

Update: Actually, I was wrong about the 4.5, but not terribly wrong. I'm actually trying to figure out how many acres would have been contained by a wall around a city in ancient Persia that was 33 stadia in length. Wikipedia [ http://en.wikipedia.org/wiki/Stadia_(length) ] tells me that 1 stade at that time was 196... show more Actually, I was wrong about the 4.5, but not terribly wrong. I'm actually trying to figure out how many acres would have been contained by a wall around a city in ancient Persia that was 33 stadia in length. Wikipedia [ http://en.wikipedia.org/wiki/Stadia_(length) ] tells me that 1 stade at that time was 196 meters, which a conversion calculator tells me is 0.1218 miles.

So, 33 stadia would be right at 4 miles (33*0.1218=4.0194).

So my real question is how many US acres would be contained in a city wall with a perimeter of 4 miles.

Randy King provided a very quick answer for 4.5 miles. Randy, taking your formula I come up with 1.27

Circumference = pi X Diameter
Area = pi X radius squared
640 Acre = 1 Square Mile
----------------------
4.0 = 3.14159d
d = 1.27 miles
r = 0.64
r^2=0.511
----------------------
A = 3.14159 * .511 = 1.61sm ~ 1028 Acres

Is that correct?