A cylindrical soda can holds about 355 cc of liquid. In this activity, we want to find the dimensions of such a can that will minimize the surface area, since this will minimize the material used to construct this can. For the sake of simplicity, assume the can is a perfect cylinder.
What are the variables in this problem? Based on the context, what restriction(s), if any, are there on these variables? You will likely find it useful to draw a picture of your cylindrical can and label your variables.
What quantity do we want to optimize in this problem? What equation describes the constraint? You need to decide which of these functions plays the role of the objective function, , and which plays the role of the constraint function, , in our discussion of Lagrange multipliers.
Use your choices for the objective and constraint equations to set up a system of equations in terms of your variables and corresponding to the Lagrange Multipliers. Find and the values of your variables that satisfy Equation this equation in the context of this problem.
Determine the dimensions of the soda can that give the desired solution to this constrained optimization problem.