A wire of length 6 is cut into two pieces which are then bent into the shape of a circle of radius [math] and a square of side [math]. Then the total area enclosed by the circle and square is the following function of [math] and [math]

If we solve for [math] in terms of [math], we can reexpress this area as the following function of [math] alone:

Thus we find that to obtain maximal area we should let [math]
To obtain minimal area we should let [math]