A Surface Integral - 3 (True or False)

Is the following statement true of false:

Given a solid with a smooth (differentiable) surface, and volume $V$ , then

$\dfrac{1}{3} \displaystyle \int_S (\mathbf{r} - \mathbf{r_0}) \cdot d\mathbf{S} = V$

where $\mathbf{r}$ is the position vector of a point on the surface of the solid, and $\mathbf{r_0}$ is an arbitrary point in space, and the integration is carried out over the solid's surface.