Answer
The equation of the surface of a cylinder can be expressed as:
$y^2+z^2=36$ for $0 \leq x \leq 2 $ with radius $6$ and height of $2$ along x-axis.
Work Step by Step
We are given the parametric equation of the cylinder as:
$r (u, v)=\lt v, 6 \cos u, 6 \sin u \gt$
and $0 \leq u \leq 2 \pi; 0 \leq v \leq 2 $
Suppose that $u=x; y=6 \cos u ; z=6 \sin u$
So, we have: $y^2+z^2=36$ for $0 \leq v \leq 2 \implies 0 \leq x \leq 2 $
Thus, the equation of the surface of a cylinder can be expressed as:
$y^2+z^2=36$ for $0 \leq x \leq 2 $ with radius $6$ and height of $2$ along x-axis.
