A slice of circular pizza has perimeter 32 inches. Denote the central angle of the slice of pizza by theta radians and the radius by x inches. What is the diameter of the pizza which give maximum area (and hence the most pizza)? Justify your answer. Show a sketch and recall that the area of the sector of a circle with central angle theta radians and radius R is 1/2R2 theta and the length of the arc cut off by such an angle has length R(theta) with the angle measured in radians again.