A cone is created by rotating an isosceles right triangle with leg length 2 about one of its legs.  Its surface area is $\pi$ times what number?
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<|im_start|>user
A cone is created by rotating an isosceles right triangle with leg length 2 about one of its legs.  Its surface area is $\pi$ times what number?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
4\sqrt{2} + 4
A cone is created by rotating an isosceles right triangle with leg length 2 about one of its legs.  Its surface area is $\pi$ times what number?
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