4. A new auditorium is built with a foundation in the shape of ¼ of a circle of radius 50 feet. Therefore, it forms a region 2 bounded by the graph of x² + y² = 502 with x≥0 and y≥0. The equations for the floor and the ceiling are given by the following. x+y 5 z=20+ xy 100 Floor: inclined plane Ceiling a) Calculate the volume of the room. This is needed to determine the heating and cooling requirements. b) Find the surface area of the ceiling.