An equilateral triangle of side 12 centimeters is rotated about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
An equilateral triangle of side 12 centimeters is rotated about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
72\pi\sqrt{3}
An equilateral triangle of side 12 centimeters is rotated about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone?
train