#### Answer

a. $2\pi x(x+3)^{2}$
b. $r=x+3$

#### Work Step by Step

a.
$2\pi x^{3}+12\pi x^{2}+18\pi x=$
...factor out the GCF.
$=2\pi x(x^{2}+6x+9)$
...write $(x^{2}+6x+9)$ as a square of a binomial.
$=2\pi x(x+3)^{2}$
b.
If $V=\pi r^{2}h$, and $V=2\pi x(x+3)^{2}$, then $h=2x,\ \pi=\pi$, which means that
$r^{2}=(x+3)^{2}$
$r=x+3$