The base of $S$ is a circular region with boundary curve $36 x ^ { 2 } + 16 y ^ { 2 } = 144$. Cross-sections perpendicular to the $x$ axis are isosceles right triangles with hypotenuse in the base. Find the volume of $S$.

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The Answer of The base of $S$ is a circular region with boundary curve $36 x ^ { 2 } + 16 y ^ { 2 } = 144$. Cross-sections perpendicular to the $x$ axis are isosceles right triangles with hypotenuse in the base. Find the volume of $S$.

The Base Of SSS Is a Circular Region with Boundary Curve 36x2+16y2=14436 x ^ { 2 } + 16 y ^ { 2 } = 14436x2+16y2=144

The Base Of $S$ Is a Circular Region with Boundary Curve $36 x ^ { 2 } + 16 y ^ { 2 } = 144$