### The land use of cities

Given a large city of one million.

Given that the agricultural land needed to feed a family of four is about one hectare.

Given that only about 30 % of land can be farmed.

Given that the population density of cities can be around 5000 inhabitants per square kilometre.

Calculate:

If the city is circle-shaped, what would its radius be in kilometres?

What would be the radius of the area around the city, needed to feed the city’s inhabitants?

If the land around the city could be farmed 100%, what would the radius of the farming area/food production area be?

Extra work:

Find out the population of a city near you, and its density.

Work out how much agticultural land would be needed to feed it according to the above.

Create a map of the city and its area around it showing how far its food circle extends.

4 Responses to “The land use of cities”
1. Martin Saar says:

Hej Steve!
Jättebra för att kommmunicera sårbarhet. Per G Berg i Living Dreams för ett liknande resonemang.
Häls
M

2. Hi Steve,
The problem breaks down like this:

A city of 1,000,000 with density 5,000 per km^2 will need 200 km^2;
for a circle with area 200 km^2, radius r = sqrt(200/pi) = 7.98 km.

If one hectare feeds four, then 250,000 arable hectares will be needed to feed 1,000,000;
if land is 30% arable, then a total of 833,333.33 (250,000/.3) km^2 will be needed.

Add to this the non-arable land (200 km^2) at the center occupied by the city itself, and the total land area occupied will be 833,533.33 km^2 – an area whose radius r = sqrt(833,533.33/pi) = 515.1 km, or, subtracting the area of the city, a torus around the city with a width 507.11 km.

If the land was 100% arable (nice!), then the total amount of land needed would be 250,000 km^2 + 200km^2 for the city = 450,000 km^2, radius r = sqrt(450,000/pi) = 378.47 km, or a torus around the city 370.49 km wide, a reduction in radius (or torus width) of 136.62 km from the 30% arable condition.

Either way, it is a staggeringly large amount of land to feed the city!

DBR