A $12^{\prime \prime}$-diameter pizza and a $16^{\prime \prime}$-diameter pizza are each cut into eight congruent slices. Jane ate three slices of the $12^{\prime \prime}$ pizza. Mark ate three slices of the $16^{\prime \prime}$ pizza. How many more square inches of pizza did Mark eat than Jane? Express your answer as a common fraction in terms of $\pi$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A $12^{\prime \prime}$-diameter pizza and a $16^{\prime \prime}$-diameter pizza are each cut into eight congruent slices. Jane ate three slices of the $12^{\prime \prime}$ pizza. Mark ate three slices of the $16^{\prime \prime}$ pizza. How many more square inches of pizza did Mark eat than Jane? Express your answer as a common fraction in terms of $\pi$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{21}{2}\pi
A $12^{\prime \prime}$-diameter pizza and a $16^{\prime \prime}$-diameter pizza are each cut into eight congruent slices. Jane ate three slices of the $12^{\prime \prime}$ pizza. Mark ate three slices of the $16^{\prime \prime}$ pizza. How many more square inches of pizza did Mark eat than Jane? Express your answer as a common fraction in terms of $\pi$.
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