A circular sheet of paper of radius 6 inches is cut into 3 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone?
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<|im_start|>user
A circular sheet of paper of radius 6 inches is cut into 3 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
4\sqrt{2}
A circular sheet of paper of radius 6 inches is cut into 3 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone?
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