Answer
Cylindrical coordinates: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$
Work Step by Step
We know that the Conversion of rectangular to cylindrical coordinate system gives: $r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$
Here, the center of the $z-axis$ of the cylindrical shell is at the origin.
This implies that the cylindrical coordinates inside the shell are bounded as:
{$(r, \theta, z) \in E|6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,-10 \leq z \leq 10$}
Thus,
Cylindrical coordinates: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$
