Section 75. The board of survey may, and in cities, upon the vote of the planning board and the city council, shall, from time to time cause plans to be made of such territory or sections of lands in the city or town as the board of survey or the planning board may deem necessary, showing thereon the location of such ways, whether already laid out or not, as, in the opinion of the board, the interest of the public may or will require in such territory, showing clearly the direction, width and grades of each way, and in cities a plan of drainage, and said board may incur such expenses as it may deem necessary therefor, not exceeding the amount appropriated for the purpose. In cities such plans shall be prepared by the city engineer, under the direction of the board. Before causing such plans to be made, the board shall give a public hearing thereon, which shall be advertised in the manner prescribed in the preceding section, and shall, after the making of any such plan, give a hearing thereon, advertised in like manner, and keep the plan open to public inspection for one month after the first advertisement of the hearing. After the hearing, and after any alterations deemed necessary by said board have been made, the same shall be approved, signed, marked, filed and attested as provided in respect to the plans mentioned in the preceding section.