Answer both problems

A rocket Liquid Oxygen $($LOX$)$ tank is made by rotating the shape shown about the $x$ axis.

Given $r=2\mathrm{.}5m$ and $L=8m$ determine the centroid of the shape shown.

The area centroid location is $\stackrel{}{x}=$ m and $\frac{?}{\text{b}\text{a}\text{r}}(Y)=$ m$.$

What is the volume of the LOX tank made by rotating this area about the $x$ axis using Pappus$-$Guldinus Volume Theorem?

The volume of the LOX tank is $$ m$3$

Assuming a uniform density, the $$ location of the center of gravity of the tank be the same as the $$ location centroid of the profile area above. $$