Starting my first build and am looking for projects to start. Is a totally round head with tiny mouth like Dr. Bunsen a challenge? He looks like solid foam! Do you think he's
hollow?

I think he is hollow. A head like his can be achieved with wedge pieces. Below is a link to a wedge pattern in Billy's gallery that was at one time on the now defunct puppetbuilding.com. 

http://puppetsandstuff.com/community/index.php?action=gallery&g2_itemId=8610

It would be very difficult to carve a perfectly round shape from a solid foam block.  There are several patterns for making spherical heads the tricky part is getting the mouth so that it sin't too difficult to operate.  The trick is making it so that it is open when the puppet is at rest.  That way the effort for the puppeteer is to shut the mouch not open it.

i think that there are pro's and con's to either way of building the head, for example, if you used the wedge pattern, there is a possibility that the wedges might not create a totally round shape, maybe slightly pointy ontop, and the if you used the carving technique, then you might be there for hours carving to find out that it doesn't operate very well. but then again, alot can be done with the wedge method and if you where using at-least 1 inch foam to construct the head, you can smooth down any imperfections after, and the carving method is absolutely brilliant if you want exactly what you are picturing, providing you have a decent amount of time and patience. but having said that, if you where covering the head with a fabric (suggestibly antron fleece) then alot can be achieved and covered, giving you a lovely clean, smooth finish to the puppet. but as Jon was saying, you would have to create the puppet with its mouth open, this helps in the long run, believe me!!
hope we are helping!!
Ben.

Thanks for the replies and thank you so much for the rounded pattern. This is truly great.  I can't wait to try this out!!!!!

This forum is truly great.  I can't believe I waited this long to try out building puppets.