Chapter 14 - Vector Calculus - 14.6 Surface Integrals - 14.6 Exercises - Page 1123: 1

$x =a \cos \theta; y=a \sin \theta$ and $z=Z$

Let us consider $Z$ be the axis parameter and the radial parameters can be written as: $\sin \theta$ and $\cos \theta$. Here, $\theta \in [0, 2\pi]$ and $0 \leq Z \leq h$ and $h$ is the height of a cylinder. Thus, the parametric description for a cylinder with radius $a$ can be expressed as: $x =a \cos \theta; y=a \sin \theta$ and $z=Z$