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 = 2 3.14 r^2 + 2 3.14 rh.
A.) 2 3.14 (3x^2 + 10x - 8)
B.) 2 3.14 (12x^2 + 7x -2)
C.) 2 3.14 (12x^2 - 2x + 13)
D.) 2 3.14 ( 12x^2 - 5x - 2)
First, plug in the given values for the radius and height into the formula.
A = 2(3.14)(3x - 2)^2 + 2(3.14)(3x - 2)(x + 3)
Expand and simplify:
A = 2(3.14)(9x^2 - 12x + 4) + 2(3.14)(3x^2 + 7x - 6)
A = 2(28.26x^2 - 37.68x + 12.56) + 2(9.42x^2 + 21.98x - 18.84)
A = 56.52x^2 - 75.36x + 25.12 + 18.84x^2 + 43.96x - 37.68
A = 75.36x^2 - 31.4x - 12.56
Therefore, the correct answer is D.) 2 3.14 ( 12x^2 - 5x - 2)