Answer
Cylindrical coordinates: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}
Work Step by Step
Let us consider the $z-axis$ to be the axis of the cylindrical shell along with the center at the origin.
Conversion of rectangular to cylindrical coordinate system gives $r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$
Thus, we have the cylindrical coordinates inside the shell:
{$(r, \theta, z) \in E|6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,-10 \leq z \leq 10$}
Hence, the Cylindrical coordinates are: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}