a sphere
A cone. A hemisphere.
A Cylinder
Cone
A cone
a cone.
curved
A cone.
Cylinder
A cone would fit the given description
a sphere
A sphere.
a rectangle
A cylinder. Technically, the curved surface of a cylinder is not called a face, only the flat surfaces, so a cylinder has 2 faces and one curved surface.
Get a ball. Draw any closed shape on it. The part inside the curve that you drew is one curved face and that is contained by the surface of the ball which is the other curved face.
sphere
A sphere has one surface that's also curved and has no base.