I have seen the derivation for the formula: h2(pi)rdr used in math textbooks. However, earlier today I had a physics problem where I needed to use the volume of a cylindrical shell of inner radius r and outer radius dr+r and length h. without remembering the formula I tried to derive it starting by determining the area of the base minus the area of the gap: A=(pi)r^2-(pi)(r+dr)^2 and then multiplying by h I could not get this in the form h2(pi)rdr starting from where I did. I understand the derivation given here: http://www.stewartcalculus.com/data...texts/upfiles/3c3-Volums-CylinShells_Stu .pdf But I'm just frustrated that I can't understand why the method I tried doesn't reduce to the correct formula. Its simply the area of the base*height! Why can't that formula be arrived at by my method???