What part lies in the first octant?

Geometry Level 3

An ellipsoid centered at the origin has semi-axes lengths of 3, 5, 10. These axes are along the vectors (-1,-1,2) , (1, -1, 0), and (1,1,1) respectively. Find the volume of the region that is both inside the ellipsoid and inside the first octant. (The first octant is where x 0 , y 0 , z 0 x \ge 0, y \ge 0 , z \ge 0 )


The answer is 181.07.

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