Let $R$ be the region bounded by the $x$-axis, the graph of $y = \sqrt{x}$, and the line $x = 4$. (a) Find the area of the region $R$. (b) Find the value of $h$ such that the vertical line $x = h$ divides the region $R$ into two regions of equal area. (c) Find the volume of the solid generated when $R$ is revolved about the $x$-axis. (d) The vertical line $x = k$ divides the region $R$ into two regions such that when these two regions are revolved about the $x$-axis, they generate solids with equal volumes. Find the value of $k$.
Let $R$ be the region bounded by the $x$-axis, the graph of $y = \sqrt{x}$, and the line $x = 4$.
(a) Find the area of the region $R$.
(b) Find the value of $h$ such that the vertical line $x = h$ divides the region $R$ into two regions of equal area.
(c) Find the volume of the solid generated when $R$ is revolved about the $x$-axis.
(d) The vertical line $x = k$ divides the region $R$ into two regions such that when these two regions are revolved about the $x$-axis, they generate solids with equal volumes. Find the value of $k$.