# Calculate the volume of a sphere

I set up myself to calculate the volume of a sphere of radius $r$ using spherical coordinates.
I found that $V=\frac{r^2\pi}{2}$. So I think I set up badly the triple integral : $V=\int_0^{2\pi}\int_0^{\pi}\int_0^r \rho \sin ^2 (\phi) d\rho d\phi d\theta$.
Edit : I just saw my error. I integrated $\rho \sin ^2 \phi$ instead of $\rho ^2 \sin \phi$.
Shouldn't you have $dV = \rho^2 \sin \phi\: d\rho\: d\phi\: d\theta$?
Also your $\rho$ is confusing; r is the standard notation.