I thought someone would bite on this problem. Here's how I done it. It appears to check. I just made up those dimensions from looking at one of those types of tankers on the road. we could've derived a general case instead.
Since the ellipse is 6 feet wide and 4 feet high, the ellipse has the equation
Solve for x in terms of y:
Now, integrate and we get:
For the general case, from
Kind of long connected and probably simplifies, but that's all I'm doing.