Pyramid maximized

Level pending

Let S A B C SABC is pyramid, such that S A ≤ 4 SA\le4 , S B ≥ 7 SB\ge7 , S C ≥ 9 SC\ge9 , A B = 5 AB=5 , B C ≤ 6 BC\le6 and A C ≤ 8 AC\le8 . Find maximum possible volume of the pyramid S A B C SABC .

7 5 7\sqrt5 8 6 8\sqrt6 4 3 4\sqrt3 10 5 10\sqrt5

Danish Ahmed by Danish Ahmed , 24, India

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