A cone is constructed by cutting a sector from a circular sheet of metal with radius 12. The cut sheet is then folded up and welded. Find the radius and height of the cone with maximum volume that can be formed in this way. Write the objective function relating V and h in a form that does not include r. 1 h³ V= 48th- (Type an expression. Type an exact answer, using as needed.) The interval of interest of the objective function is [0,12]. (Simplify your answer. Type your answer in interval notation.) The radius is r = and the height is h =. (Type exact answers, using radicals as needed.) 12 12

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