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To print out this piece you can open it in GeoGebra 3D Graphing or GeoGebra Classic, go to MENU > File > Download as > STL. A pop-up box will be opened to adjust the dimensions and thickness (3.5 mm by default, but 2 mm might be enough). The next step is opening the STL file in a 3D printer software and finally print it out. You can find more details in this tutorial or also joining this group for further issues. hint: a short way to open it either in GeoGebra Classic or GeoGebra 3D Graphing is changing the m in the URL to classic or 3d respectively, as shown in the examples below: change to or to . p.s: if you open it in the 3D Graphing mode you must hide all objects that you are not interested in printing out (like axes and the basic plane, for instance) before you download as STL.
A possible approach in using this piece is asking your students to deduct the formula of the area of the spiral (considering its "infinite" steps of recurrence) and comparing their different solutions' strategies for getting that.