Solution:
The surface area of the cylinder is expressed as
[tex]\begin{gathered} \text{Surface area = }2\pi rh+2\pi r^2 \\ \text{where} \\ r\Rightarrow radius\text{ of its circular ends} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} \text{diameter = 6}cm \\ \Rightarrow radius=\frac{6}{2}=\text{ 3}cm \\ \text{height}=\text{ 11}cm \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \text{Surface area = }2\pi rh+2\pi r^2 \\ =(2\times\pi\times3\times11)+(2\times\pi\times3\times3) \\ =66\pi+18\pi \\ =84\pi \\ \Rightarrow\text{Surface area}=263.8937829cm^2 \end{gathered}[/tex]Thus, the surface area of the cylinder is 263.8937829 square cm.