Calculus · Medium problem

Let $R$ be the region in the first quadrant bounded by the curves $y=\sqrt x$ and $y=\dfrac{x}{2}$.

• Find the area of $R$.
• The region $R$ is revolved about the $x$-axis. Find the volume of the solid generated.
• Region $R$ is the base of a solid whose cross-sections perpendicular to the $x$-axis are squares. Find the volume of this solid.
• Find the volume of the solid generated when $R$ is revolved about the line $y=-1$.