The members of the board of supervisors of a newly consolidated district are the supervisors from each of the districts that have been consolidated whose existing terms of office would last expire if the new consolidated district were not established. Those members shall determine by lot the order in which their terms of office in the consolidated district will expire. If more than three districts are consolidated, the members of the board of supervisors of the consolidated district must be determined by lot among the supervisors from the districts whose existing terms would expire last. If only two districts are consolidated, the third member of the    board of supervisors of the consolidated district must be determined by lot among the remaining supervisors from both such districts. The supervisors thus selected shall hold office until the next general election of the district and until their successors are elected and qualified. Supervisors of a consolidated district have all the powers and duties of supervisors of a soil conservation district as enumerated in this chapter. The name of a consolidated district must be determined by the new supervisors of the consolidated district.