Waltham preservation officials will hold a public hearing on Tuesday to discuss funding the final portion of a half-million-dollar project to restore a historic home. The Community Preservation Committee hearing will focus on appropriating $160,000 for the Colonial-era Wellington House, located off Trapelo Road, to finish returning the house’s interior to its original structure and décor. Once the interior restoration is finished, the building can be used as office or museum space, committee officials said. The city has been approving funds to update the exterior and foundation, according to committee officials. Mayor Jeannette McCarthy, who helped spearhead the restoration project, will be present at the hearing for questions and comment. The Waltham Historical Commission will also present updates of its projects at the meeting. The meeting will take place Tuesday at 7 p.m. at Waltham City Hall, 610 Main St. The public is welcome to give feedback at the meeting, or forward it to the committee beforehand at firstname.lastname@example.org, or by calling 781-314-3117.