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Brimful 2

Which of these infinitely deep vessels will eventually full up?


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?