Answer
Cylindrical coordinates: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}
Work Step by Step
Consider that $z-axis$ be the axis of the cylindrical shell whose center is at the origin.
Conversion of rectangular to cylindrical coordinate system as follows: $r^2=x^2+y^2$ and $\tan \theta=\dfrac{y}{x}$, $z=z$
Now, the cylindrical coordinates inside the shell are:
{$(r, \theta, z) \in E|6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,-10 \leq z \leq 10$}
Our Cylindrical coordinates are : $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}
