I came across many optimization problems in calculus asking to find dimensions of a figure that minimize or maximize something.
For example, the dimensions of a rectangle or cylinder and the answers to those problems show the lengths of sides or radius and they don't say something like "the dimensions are ….." Am I understanding problems wrong?
Example) A cylindrical can is to be made to hold 1L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can.
I just edited the question.
Best Answer
In the context of calculus problems involving optimization the dimension of an object are those lengths which completely describe the object.
For example a square is described by its side length, and a rectangle is described by the length and the width while a triangle is described either by the side lengths or by the base and height and so forth, depending on the question.
For a cube the length of one side and for a cylinder the radius of the base and the height describe the object.