"(b) Let $C$ be the solid cone with the boundary surfaces $x^2 +y^2 = z^2$ and $z = 0$. The density of the solid at point $(x, y,z)$ is $z$. Find the volume of the solid using the integrals in both the cylindrical coordinates and the spherical coordinates."
I have done this question and got an answer that is $\frac{\pi}{4z}$ in cylindrical and $\frac{\pi}{8z}$ in spherical. I took $\phi$ in spherical coordinates to be between $0$ and $\frac{\pi}{4}$. Is this correct?