The total surface area of a cylinder is given by the formula:

\(2\pi r^2 + 2\pi rh\), 

where r is the radius and h is the height of the cylinder. 

In this case, the radius r is given as 3cm and the total surface area is given as 36\(\pi\)cm2. 

Substituting these values into the formula, we get:

\[36\pi = 2\pi (3)^2 + 2\pi (3)h\]
\[36\pi = 18\pi + 6\pi h\]
\[18\pi = 6\pi h\]
\[h = \frac{18}{6} = 3\]

So, the height of the cylinder is 3cm.