Problem

Source: Uzbekistan NO 2013, P5

Tags: geometry, 3D geometry, pyramid, trigonometry, geometry proposed



Let $SABC$ is pyramid, such that $SA\le 4$, $SB\ge 7$, $SC\ge 9$, $AB=5$, $BC\le 6$ and $AC\le 8$. Find max value capacity(volume) of the pyramid $SABC$.