The shape is called sector. The formal mathematical definition of sector is the portion of a circle bounded by two radii and the included arc.
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A Cylinder
A cuboid has 6 flat faces but no curved surfaces. ..________ ./............../| /_______/.| |..............|.| |..............|./ |_______|/
Cylinder
A prism has no curved surfaces. It has 5 or more flat faces.
There can be no such shape. If there were a shape with n flat surfaces, then if you sliced off one vertex, you would have a shape with n+1 flat surfaces. So it is always possible to add one more flat surface.