Answer
$ 4\pi x^{2}+20\pi x+24\pi$
Work Step by Step
$S.A.=2\pi r^{2}+2\pi rh$
...surface area of a cylinder.
$=2\pi(x+2)^{2}+2\pi(x+2)(x+4)$
...substitute $x+2$ for $r $and $x+4 $ for $h$.
$=2\pi(x+2)(x+2)+2\pi(x+2)(x+4)$
...write $(x+2)^{2}$ as $(x+2)(x+2)$.
$=2\pi(x^{2}+2x+2x+4)+2\pi(x^{2}+4x+2x+8)$
...multiply binomials.
$=2\pi(x^{2}+4x+4)+2\pi(x^{2}+6x+8)$
...factor out $ 2\pi$.
$=2\pi(x^{2}+4x+4+x^{2}+6x+8)$
...combine like terms.
$=2\pi(2x^{2}+10x+12)$
...write in standard form.
$=4\pi x^{2}+20\pi x+24\pi$
