Which of these infinitely deep vessels will eventually full up?
Brimful
Age 16 to 18 Challenge Level
For revolution of a curve $y=f(x)$ about the $x$ axis between $0$
and $a$, the volume of revolution is
$$V=\pi\int^a_0y^2 dx$$
How can we alter this to work out the volume obtained by rotating
about the $y$ axis?