When the council of any such city having less than thirty thousand inhabitants and having a special charter shall deem it necessary to pave, macadamize, gutter, curb, grade or otherwise improve the roadway of any street, avenue or other highway not more than eight hundred feet in length so as to connect with paved, macadamized, curbed, graded or improved streets at both ends, on the same or other streets, the council shall, by resolution, declare such work necessary to be done, and shall cause the same proceedings to be had as is provided in sections 88.787 and 88.790, except that no protest may be filed. The resolution passed and published shall state the fact that anyone desiring to do so may appear before the council at a time stated therein and be heard on the question of the necessity of the work sought to be done, and if anyone does so appear he shall be heard, and the council shall by resolution state the result of such hearing to be a reaffirmance of the necessity for the doing of such work, or the contrary, as the fact may be. If no one appears, or if the council reaffirms the necessity of the doing of such work, then it shall proceed under the terms of sections 88.787 and 88.790, in the same manner as is therein provided when the abutting resident owners fail to file a sufficient protest. The work shall be done in the same manner and of the same materials as one or both of the improvements on the street or streets, avenue or highway to be thus connected is constructed, and only such work may be done as will connect similar work on said street or streets, avenues or highways.