How can I project a geometry on a curved surface and carve it out from that surface?

like the hollow carves in the rim of a tyre

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First - Create a plane off that surface

Second - Make a Sketch that you want to be projected

Final - Do a Cut-Extrude, and make your start condition Surface/Face/Plane, and select the surface to where you want your projected sketch to be on. then you can enter the depth of the cut, or you can make it go up to next suface.

 
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