# Math Help - Two ways of calculating area of a cylinder?

1. ## Two ways of calculating area of a cylinder?

Find the area of the part of the cylinder $x^2+y^2=1$ that is given by $0<= z <= 2-x^2-2y^2$.
(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 = $\int\limits_0^{2\pi } {(2 - \cos ^2 t - 2\sin ^2 t)dt}
$
(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?