Create the whole cone and remove the non-existant part.
4^2*pi*h(40 unless I'm mistaken)/3-3^2*pi*h(30)/3

3,5^2*pi*h(35)/3-3^2*pi*h(30)/3

Considering what I just wrote, it seems that it's either a double integral or a triple.

int: int: int: r/3 drad/dt dr/dt, dh/dt or something like that (i don't think this one handles the cone part correctly).