Use of the derivative of a function of one variable to optimize. Elimination of a variable in one expression using a constraint equation. We have given this problem in class and students working in groups have finished in in 20 minutes. We expect students to have some difficulty in bringing the problem to a one variable function to optimize. Future payoffs Students will improve their ability to set up and complete optimization problems.
Extensions Perhaps make two equal cones with cutting out two equal wedges.
This appears to be a function of two variables but if one writes out all the information one finds there is but one variable, we used theta - the angle of the cut sector. We offer a plot of a typical bounded region. The following code will generate the figure above. We presume a sector of angle theta and a circle of radius r. We eliminate the variable R or at least write R in terms of L and theta only.