I set up myself to calculate the volume of a sphere of radius $\displaystyle r$ using spherical coordinates.

I found that $\displaystyle V=\frac{r^2\pi}{2}$. So I think I set up badly the triple integral : $\displaystyle V=\int_0^{2\pi}\int_0^{\pi}\int_0^r \rho \sin ^2 (\phi) d\rho d\phi d\theta$.

Maybe I made an error with the order of integration, but I don't see it.

Edit : I just saw my error. I integrated $\displaystyle \rho \sin ^2 \phi$ instead of $\displaystyle \rho ^2 \sin \phi$.