My problem goes as: A gummy bear mold has a base which can be modeled by the graphs of
$x=2+\cos(2y)$ and $x=\sin\left(\frac{y}{3}\right)+4$, where the graphs are both restricted to $-5 \leq y \leq 5$.
Each plane section perpendicular to the $y$-axis is an ellipse with a $3:5$ ratio between width to height ratio (consider the x-axis to be width).
Find the full surface area of a gummy bear shaped in this mold.
I know how to find the flat surface area; it is just the area between the two graphs.
However, how would I go about finding the surface area of the top? I know how to find the volume, but aren't there slant heights and whatnot involved?
Is there a general formula / procedure for finding surface area of regions with known cross sections, just like there is for volume?