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Gaokao Math Practice Question

10. (5 分) 在封闭的直三棱柱 $A B C-A_{1} B_{1} C_{1}$ 内有一个体积为 $V$ 的球, 若 $A B \perp$ $B C, A B=6, B C=8, A A_{1}=3$, 则 $V$ 的最大值是 $(\quad)$

  1. A.$4 \pi$
  2. B.$\frac{9 \pi}{2}$
  3. C.$6 \pi$
  4. D.$\frac{32 \pi}{3}$

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