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Volumes of solids of known cross-section

The base of a solid SS is the region bounded by the ellipse 4x2+9y2=364x^2+9y^2=36. Cross-sections perpendicular to the yy-axis are rectangles with heights twice as large as their bases.
Determine the exact volume of solid SS.
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4