The base of the cylinder has area πr² = 36π ≈ 113.10 (assuming the radius is 6, and not the diameter, that's not clear to me).
If you take the paper wrapped around the cilinder, it would be a rectangular piece of height 12 and length equal to the circumference of the cilinder, being 2πr = 12π, so the area would be 12*12π=144π ≈ 452.39.
So in total this is 452.39+113.10 ≈ 565.49, that's answer D.
