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Calculus help dimensions to be used for minimum cost?

A silo (base not included) is to be constructed in the form of a cylinder with a hemisphere on top. the cost of the construction per square unit of surface area is twice as great for the hemisphere as it is for the cylindrical sidewall. determine the dimensions to be used if the volume is fixed and the cost of the construction is to be kept at a minimum. neglect the thickness of the silo and the waste in construction. i really have no clue how to solve this. im also not sure what it means by hemisphere on top.. any help would be greatly appreciated. also must prove with first or second derivative test.


A hemisphere is half a sphere, and to do this question you must figure out an equation for a graph related to whatever information they provide. Then, minimum cost on the graph would be a turning point. Thus, dy/dx = 0. To find the nature of the point, for it to be a minimum point, d2y/dx2 must be greater than 0. Hope you can figure out the rest on your own. Good luck!

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