Let $f ( x ) = \sqrt { x - 4 }$.

1. Calculate the area of the region bounded by $y = f(x)$, the $x$-axis, and $x = 8$.

   Hint (a):

   Before you set up an integral, sketch the graph and shade the region.

2. If the line $x = c$ divides the region from part (a) into two pieces of equal area, what is the value of $c$?

   Hint (b):

   $\int_{4}^{c}f(x)dx=\frac{1}{2}\text{ of your answer to part (a).}$

   Solve for $c$.

3. Calculate the volume of the solid that is formed by rotating the region described in part (a) about the $x$-axis.

   Hint (c):

   Use disks.

4. If a plane perpendicular to the $x$-axis at $d = x$ divides the solid in part (c) into two parts of equal volume what is the value of $d$?

   Hint (d):

   Refer to the hint in part (b) and follow a similar process using a generic volume formula instead of a generic area formula.

   Step (d):

   $\text{Solve:}\int_4^d \pi(\sqrt{x-4})^2dx=\int_d^8\pi(\sqrt{x-4})^2dx$