A hole of radius $r$ is bored through a cylinder of radius $R > r$ at right angles to the axis of the cylinder. Which of the following integrals represents the volume cut out?

A. $\displaystyle 4\int_{-r}^{\,r} {\sqrt{r^2-y^2}\sqrt{R^2-y^2}}\,dy$
B. $\displaystyle 4\int_{-r}^{\,r} {\sqrt{r^2-y^2}\sqrt{R^2+y^2}}\,dy$
C. $\displaystyle 2\int_{-r}^{\,r} {\sqrt{r^2-y^2}\sqrt{R^2+y^2}}\,dy$
D. $\displaystyle 2\int_{-r}^{\,r} {\sqrt{r^2-y^2}\sqrt{R^2-y^2}}\,dy$
E. $\displaystyle 2\int_{-r}^{\,r} {\sqrt{r^2+y^2}\sqrt{R^2+y^2}}\,dy$
F. $\displaystyle 4\int_{-r}^{\,r} {\sqrt{r^2+y^2}\sqrt{R^2-y^2}}\,dy$
G. $\displaystyle 2\int_{-r}^{\,r} {\sqrt{r^2+y^2}\sqrt{R^2-y^2}}\,dy$
H. $\displaystyle 4\int_{-r}^{\,r} {\sqrt{r^2+y^2}\sqrt{R^2+y^2}}\,dy$