The surface area of a cylinder is given by the polynomial 2*pi*r + 2*pi*h and a cylinder has a radius of 2 centimeters, how do you find the surface area of the cylinder?

Surface area $= 2 \pi \left(2 + h\right)$
Since we haven't been given the height ($h$) for the cylinder,
the best we can do is provide a general formula replacing $r$ with $2$ in terms of a variable $h$
$\textcolor{w h i t e}{\text{XXXX}}$${A}_{c y l \in \mathrm{de} r} = 2 \pi \left(2\right) + 2 \pi h$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 2 \pi \left(2 + h\right)$