How to sketch the region $D = \{(x,y,z) \in \mathbb{R}^3: max\{1, \sqrt{x^2+y^2}\} \leq z \leq 2\} $

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Question: How to sketch the region $D = \{(x,y,z) \in \mathbb{R}^3: max\{1, \sqrt{x^2+y^2}\} \leq z \leq 2\} $

So far by plotting $ z=1$, $z=2$ and $z= \sqrt{x^2+y^2}$ I think the region could be a cone bounded by the planes $ z=1$ and $z=2$ however I am not sure if this is the correct reasoning as I am not really taking the max function into account.

What does this region look like in the 3-D plane?