Upon filing with the City Clerk-Treasurer an application for consideration of zoning request, a date must be set for a hearing thereon, which shall be not later than 45 days from the date of filing, and shall hear such persons as wish to be heard either in person or in writing. Notice of any such hearing shall be mailed not less than 10 days before the date of hearing to each person who filed the request, and to each owner of property situated wholly or partly within 350 feet of the property to which the request relates.