[schoen]

If you want to model a city as a circle, you should probably instead use a radius where half of the area of the circle lies within that radius. When you halve the radius, you divide the area by four!

For example, the area of a circle with radius 15 km is about 707 km², while the area of a circle with radius 7.5 km is only about 177 km². If the population density by unit land area is evenly distributed, this circle will only enclose a quarter of the city's population, rather than half.

I think an interesting future limiting factor is air traffic from delivery drones. Right now it seems absurd to worry about that because there are no delivery drones flying, but if this method becomes popular, the presence of other drones in the airspace could limit delivery drones' mobility.

[Y_Y]

You make a good point about circles.

I'd like to add that the pi r^2 circle we know and love isn't the only one. It depends on the "metric" which in that case is Euclidean ("as the crow flies"). If you have have traffic rules, like only flying certain routes you get a different shape circle and a different area as a function of radius. A famous example is the "Manhattan" metric where you drive around on a square grid. In this case the "circle" looks just like a square and has area 4 r^2.