The surface area (A) of a cylinder is given by the formula A = 2πr² + 2πrh, where r is the radius of the cylinder and h is its height.
In this case, the radius of the cylinder is 3x - 2 cm, and its height is x + 3 cm. Substituting these values into the formula, we get:
A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
Simplifying this expression, we get:
A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
A = 24πx² - 10πx - 12π
So the surface area of the cylinder is 24πx² - 10πx - 12π.