Answer
$ 4\pi x^{2}+22\pi x+28\pi$
Work Step by Step
$(x+2)$- radius of the cylinder
$(x+5)$-height of the cylinder
$S.A.=2\pi r^{2}+2\pi rh$
...surface area of a cylinder.
$=2\pi(x+2)^{2}+2\pi(x+2)(x+5)$
...substitute $x+2$ for $r $ and $x+5 $for $h$.
$=2\pi(x+2)(x+2)+2\pi(x+2)(x+5)$
...write $(x+2)^{2}$ as $(x+2)(x+2)$.
$=2\pi(x^{2}+2x+2x+4)+2\pi(x^{2}+5x+2x+10)$
...multiply binomials.
$=2\pi(x^{2}+4x+4)+2\pi(x^{2}+7x+10)$
...factor out $ 2\pi$.
$=2\pi(x^{2}+4x+4+x^{2}+7x+10)$
...combine like terms.
$=2\pi(2x^{2}+11x+14)$
...write in standard form.
=$ 4\pi x^{2}+22\pi x+28\pi$
