The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2pi r2 + 2 pi rh.
A) 2spi (3x2 + 10x – 8)
B) 2 pi (12x2 + 7x-2)
C) 2 pi (12x2 -2x +13)
D) 2 pi (12x2 -5x -2)
To find the surface area of the cylinder, we can substitute the given values into the formula A = 2pi r^2 + 2 pi rh.
The radius of the cylinder is 3x – 2 cm, so we substitute this value into the formula: A = 2pi (3x-2)^2 + 2 pi (3x-2)(x+3).
Simplifying the equation: A = 2pi (9x^2 - 12x + 4) + 2 pi (3x^2 + 5x - 6)
Combining like terms: A = 2pi (9x^2 + 3x^2 - 12x + 5x + 4 - 6)
Simplifying further: A = 2pi (12x^2 - 4x - 2)
Therefore, the correct answer is option D) 2 pi (12x^2 - 5x - 2).