Find the area of the part of the cylinder that is given by .

(Hint: parametrize the surface.)

I did manage to calculate the correct area by doing the following:

Cylinder parametrization in xy-plane:r(t)=(x(t), y(t)) with x(t)=cos(t), y(t) = sin(t)

Insert x(t) and y(t) in paraboloid equation to get area = (ds of r(t) is 1*dt)

How would you calculate the area by parametrizing the surface? For starters, how do you parametrize the surface?