Answer
$ 24\pi x^{2}+72\pi x+54\pi$
Work Step by Step
$h=2r=2(2x+3)=4x+6$
$S.A.=2\pi r^{2}+2\pi rh$
...surface area of a cylinder.
$=2\pi(2x+3)^{2}+2\pi(2x+3)(4x+6)$
...substitute $2x+3$ for $r $and $4x+6 $ for $h$.
$=2\pi(2x+3)(2x+3)+2\pi(2x+3)(4x+6)$
...write $(2x+3)^{2}$ as $(2x+3)(2x+3)$.
$=2\pi(4x^{2}+6x+6x+9)+2\pi(8x^{2}+12x+12x+18)$
...multiply binomials.
$=2\pi(4x^{2}+12x+9)+2\pi(8x^{2}+24x+18)$
...factor out $ 2\pi$.
$=2\pi(4x^{2}+12x+9+8x^{2}+24x+18)$
...combine like terms.
$=2\pi(12x^{2}+36x+27)$
...write in standard form.
=$ 24\pi x^{2}+72\pi x+54\pi$
