Answer: [tex](24\pi x^2 - 10\pi x - 4\pi) [/tex] square centimeters
Explanation:
Let
[tex] r = \text{radius of the cylinder} = 3x - 2
\newline \indent h = \text{height of the cylinder} = x + 3 [/tex]
Then the surface area of the cylinder is given by
[tex]A = 2\pi r^2 + 2\pi rh
\newline \indent = 2\pi r (r+h)
\newline \indent = 2\pi (3x - 2) (\left ( 3x - 2 \right ) +\left (x + 3 \right ))
\newline \indent = 2\pi (3x - 2) (4x + 1)
\newline \indent = 2\pi (12x^2 - 5x - 2)
\newline \indent \boxed{A = (24\pi x^2 - 10\pi x - 4\pi)cm^2}
[/tex]
