General Cylinder in Cone Problem: A given cone has a cylinder inscribed in it, with its
Chapter 8, Problem 28(choose chapter or problem)
General Cylinder in Cone Problem: A given cone has a cylinder inscribed in it, with its base contained in the base of the cone. a. How should the radius of the cone and cylinder be related for the lateral surface of the cylinder to maximize its area? Justify your answer. b. Find the radius of the cylinder that gives the maximum total area. c. If the cone is short and fat, the maximum total area occurs where the height of the cylinder drops to zero and all the material is used in the top and bottom bases. How must the radius and height of the cone be related for this phenomenon to happen?
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