A decorative oak post is 24 inches long and is turned on a lathe so that its profile is sinusoidal as shown in the figure below.

In this figure, $r_0 = 3$ inches and $a_0 = 8$ inches.

(a) Describe the surface of the post parametrically using cylindrical coordinates and the parameters $s$ and $t$.
$x(s,t) =$ ,
$y(s,t) =$ , and
$z(s,t) =$ , where
$\le s\le$ and
$\le t\le$ .

(b) Find the volume of the post.
volume =
(Include units.)