Originally Posted by

**arbolis** I'm having an extremely hard time trying to calculate the volume of the cone given by $\displaystyle (z-1)^2=\frac{x^2}{2}+y^2, 0\leq z \leq 1$.

I've tried to draw it in the $\displaystyle xyz$ plane : its generators cross when $\displaystyle z=1$, $\displaystyle x=y=0$. In the $\displaystyle xy$ plane its cross section is an ellipse centered at the origin, whose semi major axis is worth $\displaystyle 1$ unit and its semi minor axis is worth $\displaystyle 1/2$. But I'm not sure I've done it right. Also I have a big problem : when using cylindrical coordinates, $\displaystyle \theta$ goes from $\displaystyle 0$ to $\displaystyle 2\pi$, $\displaystyle z$ goes from $\displaystyle 0$ to $\displaystyle 1$ but $\displaystyle r$ goes from $\displaystyle 0$ to ... I'm unable to find it. I guess I must find some equation of generators, but still, the cone is not circular (cross section with the xy plane), making it difficult for me to find its volume.