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Gaokao Math Practice Question

已知三棱雉 $S-A B C$ 的所有顶点都在球 $O$ 的表面上, $\triangle A B C$ 是边长 为 1 的正三角形, $S C$ 为球 $O$ 的直径, 且 $S C=2$, 则此三棱雉的体积为 ($\qquad $)

  1. A.$\frac{1}{4}$
  2. B.$\frac{\sqrt{2}}{4}$
  3. C.$\frac{\sqrt{2}}{6}$
  4. D.$\frac{\sqrt{2}}{12}$

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