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A manufacturing plant produces the cardboard cut outs that will be used to wrap ice cream...

A manufacturing plant produces the cardboard cut outs that will be used to wrap ice cream cones. Circles with a radius of 6 inches are punched out of a sheet of cardboard. Next, a sector of the circle must be cut out from the circle so that the cardboard can be rolled up into a cone. To determine the angle of the sector that needs to be cut out to maximum the volume of the cone, one must calculate the radius and height of the cone that yields the maximum radius. (Reminder: your final answer should include an angle, radius and height).

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