Let $R$ be the region enclosed by the graph of $y = \sqrt{x-1}$, the vertical line $x = 10$, and the $x$-axis.\\
(a) Find the area of $R$.\\
(b) Find the volume of the solid generated when $R$ is revolved about the horizontal line $y = 3$.\\
(c) Find the volume of the solid generated when $R$ is revolved about the vertical line $x = 10$.