Green Areas - Task

The diagram contains three plans for building a new circle-shaped town with a radius of 1 kilometer. The colored circles inside are the building zones; the rest is intended to be a green area where no building will be allowed. The planners want the percentage of green area to be as large as possible. For each plan:
  • Construct a function describing the dependence of the percentage of the built-up area on circle dimension.
  • What should the circle sizes be for the built-up area to be as small as possible?
  • Check whether the conclusions you reached by investigating the functions are consistent with the measurements that appear in the figures.