Hello, mathman66!

Are you sure of the wording of this problem?

A circle of radiusr, you want to cut out a slice from the middle

(like cutting a piece of pie) that makes 0 < θ < 2π, and has perimeterP.

Maximize the area of this slice.

If the radiusris given and the perimeterPis given,

. . the area of the sector is determined; it is aconstant.

In fact: .A .= .½r(P - 2r)