#1
An architect is drawing up plans for a mini- theatre. The diagram shows the plan of the base which consists of a rectangle of length 2y metres and width 2x metres and a semicircle of radius x metres which is placed with one side of the rectangle as diameter.The architect decides the base should have a perimeter of 100 metres.(a) Show that the area A square metres of the base is given by A100x- 2x^2 - 1/2 (3.141592654)x^2(b) Given that x can vary, find the value of x for which dA/dx = 0 anddetermine the corresponding value of y, giving your answers to 2 significantfigures.(c) Find the maximum value of A and explain why this value is a maximum.
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