The Answer Would Be 64 because if you divide 8/4.5 its equal to 64/36.
Plug
into the equation of the ellipsoid:

Complete the square:

Then the intersection is such that


which resembles the equation of a circle, and suggests a parameterization is polar-like coordinates. Let



(Attached is a plot of the two surfaces and the intersection; red for the positive root
, blue for the negative)
A cylinder is 12 feet high has a diameter of 10 feet in cubic feet
3 and 4/9 would be the answer to this.