I'm currently in the chair donating plasma so I'm sorry for lack of pictures or misspellings or anything.
I'm trying to find the volume of a solid with an elliptical base (x^2)/49 + (y^2) = 1 using cross sections that are an isosoceles right triangle with one of the short legs on the base of the ellipses. I've gotten three different answers trying to solve this using both the formulas we derived in class for this particular type of problem as well as doing the question from scratch (finding the area function of the cross section and taking the definite integral). I'm using 7=a and 1=b and using the formula 4/3 * ab^2 I got 56/3. When I did the problem from scratch, I got different answers depending on if I used s=y or s=2y, 28/3 and 112/3 respectively.
I don't really understand when s should equal 2y or when it should equal y. We've done problems in class where we used both but I can't tell when to use which. I think therein lies the issue I'm having, but I really don't know. Can someone help me solve the original question, and maybe also explain why we'd use s=y vs s=2y?