Sphere

Slicing through the centre produces the largest possible circle. Slicing anywhere else produces smaller circles.

Cylinder

Either of the end faces of the cylinder are already the largest circle so no cutting needs to be done, although the same size circle can be produced by cutting parallel to these faces. Making a cut which is not parallel to the circular faces and which does not pass through either of these faces produces a “stretched circle” (ellipse). If the cut does go through the circular face/s, circle segment/s and an ellipse will be made.

Cone

One of the faces of the cone is already the largest circle so no cutting is necessary. This is the only way to obtain the largest possible circle. Making a cut which is not parallel to the circular face and which does not pass through this face produces a “stretched circle” (ellipse). If the cut does go through the circular face, a circle segment and an ellipse will be made.

NB The smallest circle could in theory be cut from either the circle or the cone, but the cone may be easier as it already has a "point".

Cutting parallel to the circular face of the cone will give gradually smaller and smaller circle cross sections as you go towards the tip.

Making two cuts could also give circle sectors.