A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50 feet. So, it forms a region R bounded by the graph of x2 +y² = 50² with x >= 0 and y>= 0. The following equation models for the floor and ceiling. x+y Floor: z = 5 ху Ceiling: z = 20 + 100 Calculate the volume of the room which is needed to determine the heating and cooling requirements b. Find the surface area of the ceiling

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