What's the parametrization for this set $z^2 = x^2+y^2$?

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Given $M = \{(x,y,z) \in \mathbb{R}^3 | \quad z^2 = x^2+y^2, \quad 1<z<2\}$.

What's the parametrization?

Is it $\left(\begin{array}{cc} x \\ y \\ \sqrt{x^2+y^2}\end{array}\right), \quad \text{where} \quad [x,y] \in \left(\sqrt{\frac{1}{2}},\sqrt{2}\right)$ ?