The model pictured on the left is the solid obtained by revolving the region between the graph of y=4-x^2 and the x-axis on [0,2] around the y-axis, and the model on the right is an approximation of that solid using eight shells. For more information about the math behind approximating volumes with shells, see the link below.

MakerHome, Day 237: http://makerhome.blogspot.com/2014/04/day-237-shellmaker.htmlUPDATE: Now with a handy base to match the Taalman/Kohn calculus book! MakerHome, Day 243: http://makerhome.blogspot.com/2014/04/day-243-base-for-shell-models.html