If, after the formation of a maintenance district, additional improvements of the same type or nature are constructed within the boundaries of such district, the board of supervisors shall adopt a resolution declaring its intention that the cost of maintaining and operating such additional improvements shall be borne by the existing maintenance district. It shall fix a time and place for a hearing on such resolution, at which hearing any and all persons having any objections to the things proposed to be done may appear and be heard. The resolution shall contain a statement of the estimated annual cost of maintaining and operating such additional improvements.