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

Short Answer

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 $S$ .