So the surface area of a cylinder is:
Since we are taking off the top of the cylinder we can change it to:
Next we need the surface area for a cone, minus the area of the base of the cone.
Again, we don't need the base of the cone, so we get:
This formula requires a value 's' which is the diagonal length (straight dotted line in your picture). We get this from Pythagoras.
There we are! We have everything we need. So, the surface area of our modified cylinder is:
At least, that's what I get. Hope it helps!