I would like to make a circular shelf.
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Cut out the shape and size of shelves in the form of a template. I take it you are looking for Flat backed elongated oval shelves? These could be trimmed with thin MDF to the front (Jali make many trims that may be suitable.
You want two things that are mutually exclusive. You want circles that are 24"in diameter but only 3" deep? So what you want is a 24" circle that has had 3" cut off the edge? That means your three inch shelf will go from nothing to 3 inches in the middle. I am not a good enough mathematician to tell you how long such a shelf would be. . . but it would be pretty short. Why not make shelves 24" long, by 3" deep and round off the ends?
I think you want to make a hoop shelf.
https://abeautifulmess.com/2014/10/make-a-hoop-shelf-in-an-hour.html
http://www.newblooming.com/2015/04/diy-circle-wood-shelf.html
https://www.decoist.com/2014-10-07/diy-round-shelf-idea/
https://www.google.com/search?q=how+to+make+a+circular+wooden+shelf&tbm=isch&tbo=u&source=univ&sa=X&ved=2ahUKEwiow6Oz7JTbAhUKq1kKHS2QACIQsAR6BQgBEIEB&biw=1016&bih=642
Many hardware stores sell precut wooden circles, I think they're intended for small table tops, usually 24-36" dia. Then you could attach a thin strip of wood veneer to the exposed edge of the plywood.. it can be glued and clamped on. If you don't have clamps, then wrapping it with soft cord or taping it with removable tape every inch would hold it smoothly.
I know it a hardboard. Comes in 1/8" and 1/4". What you could do is use the hardboard (dpi) and make your circle. Then laminate more hardboard around the first one with wood glue. Two or three layers would get your thickness. I have laminated thin strips of wood when ever I did a project that had bent wood in it.