1. The problem statement, all variables and given/known data Inscribe in a given cone, the height h of which is equal to the radius r of the base, a cylinder (c) whose total area is a maximum. Radius of cylinder is rc and height of cylinder is hc. 2. Relevant equations A = 2πrchc + 2πrc2 3. The attempt at a solution r = h ∴ hc = r - rc A = 2πrc(r - rc) + 2πrc2 To get the maximum of this area I will find the radius rc when the growth of the area is zero. dA/drc = 0 = 2πr What does this result mean? I don't understand how 0 = 2πr makes sense as a result from a derivation. What kind of information does this result give me geometrically? How can I know that there is no maximum area to the cylinder as my answer sheet tells me.