Find the maximum volume of a cone that fits inside a sphere of radius 1.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the maximum volume of a cone that fits inside a sphere of radius 1.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{32\pi}{81}
Find the maximum volume of a cone that fits inside a sphere of radius 1.
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