$2$: Let $R$ be the region bounded by the graph $y=\sqrt[\phantom{2}]{x},x=0,y=2.$ Let $E$ be the solid generated by revolving $R$ about the line $y=0.$ Set up $($but do not evaluate$)$ an integral to find the volume of the solid $E$ by the following steps with the shell method:

a: Sketch the region R and also please make a graph for it using the shell method.

b: Determine the direction$/$orientation of the cylindrical sheel and then determine whether we are using $dx$ or $dy$ for the thickness.

c: What is the expression of the surface area of the cylisalrical shell in terms of $x$ and$/$or $y?($This depends on your answer of the previous question$)$

ds Set up the integral to calculate the volume of the solid. $($Do not need to evaluate the integral$)$