From Equation to Volume

Geometry Level pending

An ellipsoid is specified by its equation:

162 x 2 + 266 y 2 + 74 z 2 180 x y + 36 x z 164 y z = 1296 162 x^2 + 266 y^2 + 74 z^2 - 180 x y + 36 x z - 164 yz = 1296

Its volume is n π n \pi for a positive integer n n . Find n n .


The answer is 48.

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