To figure this out, you just have to go back to the old formula of area = pi*r^2. In this equation, r is the radius of the circle.
So, we know the area of the circle so we set up the equation
314 = pi*r^2.
So now we need to divide both sides by pi which is, happily enough, 3.14. 314/3.14 is 100.
So 100 equals r^2. So to find r (the radius) we take the square root of 100, which is 10.
So the radius of the circle is 10 miles.