Multivariate Calculus: multivariate calculus – #22702


Question: Suppose you want to design a closed cylindrical container of radius r and height h that holds a fixed volume C and has the smallest possible surface area. Show what relationship must always be true between the radius r of the container and the height h, no matter what the value of C is. (Show all work.) Volume of a cylinder: V = pi*r^2*h; surface area = 2*pi*r^2 + 2*pi*r*h. (Note: You don’t have to solve for r and h in terms of C, but just show the relationship between the two that would hold true for the cylinder with minimum surface area and constant volume C.)





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