Part Il: Free response problems. Your solution should include a fully detailed FBD when applied.

Problem $4$: For the shaded area shown below:

a$)$ Determine the $\frac{?}{\text{b}\text{a}\text{r}}(Y)$ coordinate of the centroid. $($use a table to organize your solution$).$

b$)$ Determine the volume of the solid formed by revolving the shaded area $270$ about the $x$ axis. $(30$ points$)$