In calculating the volume bounded by cylinders $x^2 + y^2 = r^2$ and $z^2 + y^2 = r^2$, the following equation is usually derived:

$$\iint\limits\_{D} f(x,y) \ dA = \int\limits\_{-r}^{r}\int\limits\_{-\sqrt{r^{2}-y^{2}}}^{\sqrt{r^{2}-y^{2}}} f(x,y) \ dx dy$$

leading to $$\int\limits\_{-r}^{r}\int\limits\_{-\sqrt{r^{2}-y^{2}}}^{\sqrt{r^{2}-y^{2}}} 2\sqrt{r^{2}-y^{2}} \ dx dy = \frac{16}{3}r^{3}$$

But I cannot understand why there is $2$ in front of $\sqrt {r^2-y^2}$. Can anyone tell me why $2$ is needed?