$4.$ Use the Cylindrical Shells method to find the volume of the solid resulting from rotating the region bound by the lines specified below around the indicated line:

$\backslash ($ x$=($y$-3)^\{2\},$ x$=4$ ; $\backslash )$ about the line $\backslash ($ y$=1\backslash )$

$(1)$ Draw a diagram to the best of your ability and show all work. $(2)$ Why is Cylindrical Shells a good choice for computing this volume? $(3)$ Set up the integral and completely solve for the resulting volume.