Minimizing the Surface Area of a Cylinder with a Fixed Volume

A common optimization problem faced by calculus students soon after learning about the derivative is to determine the dimensions of the twelve ounce can that can be made with the least material. That is, the problem is to find the dimensions of a cylinder with a given volume that minimizes the surface area. Use the slider to adjust the shape of the cylinder and watch the surface area fluctuate about the minimum of the surface area function.