Region $R$ is revolved about the line $y=1$ to form a solid of revolution.
a. What is the radius of a cross section of the solid at a point $x$ in [0,4]$?$
b. What is the area $A(x)$ of a cross section of the solid at a point $x$ in [0,4]$?$
c. Write an integral for the volume of the solid.