(30 Points Total) Suppose a new auditorium is to be built with a foundation in the shape of a quarter-circle having a radius of 50 feet. (That is, the quarter-circle is from a whole circle having a radius of 50 ft .) Suppose, in addition, that the floor and ceiling are each modeled on the following equations: The floor: Z = (1/5) ( x +y) The ceiling: z =20 +(7100) xy Use the above information to answer Parts (a) and (b) below. a) (15 Points) Determine the surface area of the auditorium ceiling. Your answer must be accurate to at least two decimal places. Note: You must use methods discussed from the chapters and sections covered by this exam. If your work makes use of methods not discussed in those chapters and sections, or is based upon concepts/principles from other chapters or sections of the text not covered by this exam, you will receive no credit. Your Answer: Ceiling Surface Area =