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The surface area of a cylinder is
[tex]A=2\pi rh+2\pi(r)^2[/tex]Replacing the given information, we have
[tex]\begin{gathered} A=2\cdot\pi\cdot6\cdot7+2\cdot\pi(6)^2 \\ A=84\pi+72\pi \\ A=156\pi(cm)^2 \end{gathered}[/tex]