The board of public works shall cause to be prepared by a registered engineer, plans showing the project and an estimate of the cost thereof. Upon receipt of such plans and estimate the board of public works shall order the same to be filed with the director of public works and if it shall desire to proceed with the said project, it shall by resolution tentatively so declare and also tentatively designate the special assessment district against which the cost of the project is to be assessed. The board of public works shall then fix a time and place when and where it will meet and hear any objections to the improvement and to the special assessment district therefor, and shall cause notice of the hearing to be given by the publication thereof twice prior to the hearing in a newspaper circulating in the special assessment district, the first publication to be at least 10 days prior to the time of the hearing. The notice shall state that the plans and estimate are on file with the director of public works for public examination and shall contain a description of the proposed special assessment district. At the time of the hearing, or at any adjournment thereof which may be without further notice, the board of public works shall hear any objections to the improvement and to the special assessment district. The board of public works may revise, correct, amend or change the plans, the estimate of cost or the special assessment district. No final action shall be taken in respect to the addition of any property to the district or to increasing the estimated cost in excess of 10% of the original estimate, until after a new hearing upon notice given as above provided.