Answer:
[tex]S(x)=32\pi x^2+96\pi x+72\pi[/tex]
Step-by-step explanation:
The surface area of a cylinder is given as [tex]S.A=2\pi r(r+h)[/tex]
We have that the radius of the box is [tex]r=2x+3[/tex] inches.
The height of the gift box is three times the radius.
[tex]\implies h=3(2x+3)\\\implies h=6x+9[/tex]
We substitute into the formula to get:
[tex]S.A=2\pi (2x+3)(2x+3+6x+9)[/tex]
We simplify the last parenthesis to get:
[tex]S.A=2\pi (2x+3)(8x+12)[/tex]
We expand the last two binomial factors to get:
[tex]S.A=2\pi(16x^2+48x+36)[/tex]
We expand further to get:
[tex]S.A=32\pi x^2+96\pi x+72\pi[/tex]
