I found the following problem in a Math Olympiad book:
I know we could find the volume considering that the figure is symmetric and using a solid of revolution and an integral, the problem is that they're not giving any information about the small radius of the top of the bottle nor about the rounded part. Any suggestions to solve this problem?
Hints:- transform according to the question. function $1$ is $y=\frac{r}{2}$. Please scale elliptical part and bottle neck part accordingly. And the entire function is defined in $0\leq x \leq h$. Apply in the formula $V=\pi \int_{0}^{h}y^2 dx$.