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[Steps Shown] Suppose that we cut out a sector of a circle (the dotted lines in the diagram below), so that when the dotted lines are glued together they

Question: Suppose that we cut out a sector of a circle (the dotted lines in the diagram below), so that when the dotted lines are glued together they make a right circular cone. If the radius of the original circle is 1 unit, determine the angle $\theta$ so that

the volume of the cone is maximal.

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[Steps Shown] Suppose that we cut out a sector of a circle (the dotted lines in the diagram below), so that when the dotted lines are glued together they

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