Question 3 [14 marks] 3 marks 3 marks 3 marks 5 marks An auditorium is being designed consisting of a rectangular region with a semi- circle at each end as shown

in Figure 4. Figure 4: Illustration of the shape of the auditorium. If the perimeter of the auditorium has to be 400 m. Complete the following ques- tions. a) Show that: c) Find where P is the perimeter. b) Show that area of the auditorium can be calculated as follows: A(r) = 400r-xr². P = 2x + 2y, dA d²A dr (3) (4) d) Using calculus find the dimensions of the auditorium (r and y) which max- imises the area.

Fig: 1