Alex from Cutthorpe Primary School and Lucy from Caversham Primary sent in very clear solutions to this problem. Alex says:

To make a large circle from the cylinder and cone just use the flat faces of these shapes.

Lucy adds:

You would cut the sphere in the exact centre to get the largest possible circle from the sphere (the cut would have to be in the absolute exact centre).

She goes on to say:

You would use the cone to make a very small circle for printing. You would cut it at the top of the point.
If you cut the cone straight down from the point, you would find that the face would now be a semi-circle and the new face would be a type of triangle.
If you cut the cylinder down from the face you would find that the face was a semi-circle and the new face would be a rectangle.
If you cut the sphere in any place the face would still be a circle.

With two cuts, Alex suggests that you could cut the rectangle you made earlier (from the cylinder) into a square.

Naomi, who is Home Educated, suggests that you could make the biggest possible circle by rolling the cone around on its side, keeping the vertex as the centre of the circle. What a great idea.

Thank you also to A from MLC in Australia who sent a full solution.  (He/she didn't give us a full name.)

Are there any other possibilities? Let us know if you find any.