We need to find the surface area of the given cylinder.
The surface area of a cylinder is the sum of the areas of the top and bottom bases and of the lateral surface.
The areas of the bases of a cylinder with radius r are, each, given by:
[tex]\pi r²[/tex]
And the area of the lateral surface of a cylinder with a radius r and a height h is given by:
[tex]2\pi rh[/tex]
Thus, the total surface area of a cylinder is:
[tex]\pi r²+\pi r²+2\pi rh=2\pi r(r+h)[/tex]
In this problem, we have:
[tex]\begin{gathered} r=2\text{ cm} \\ \\ h=7\text{ cm} \end{gathered}[/tex]
Thus, the surface area is given by:
[tex]2\pi\cdot2\text{ cm}(2\text{ cm}+7\text{ cm})=4\pi(9\text{ cm})\text{ cm}=36\pi\text{ cm^^b2}[/tex]
Answer: 36π cm²
