The diagram shows a piece of wire of length 64 m which is bent to form a semicircle of radius \(4r\) m and a rectangle of length \(2x\) m.
Express \(x\) in terms of \(r\) and \(\pi\).[1]
Hence, show that the area, \(A\) m\(^2\), of the figure is \(256r-32r^2-8\pi r^2\).[2]
Given that \(r\) can vary, find the value of \(r\) which gives a stationary value of \(A\). Give your answer correct to 2 decimal places.
Determine whether this value of \(r\) gives a maximum or minimum value for \(A\).[4]