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Gaokao Math Practice Question

设 $A, B, C, D$ 是同一个半径为 4 的球的球面上四点, $\triangle A B C$ 为等 边三角形且面积为 $9 \sqrt{3}$, 则三棱雉 $D-A B C$ 体积的最大值为($\qquad$)

  1. A.$12 \sqrt{3}$
  2. B.$18 \sqrt{3}$
  3. C.$24 \sqrt{3}$
  4. D.$54 \sqrt{3}$

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