Volumes of Revolution Cross Sections

314159265
Wed, 28 Apr 2010 23:08:14 +0000

Umm, the key to doing these, in my opinion, is to make a sketch graph of the cross section. Identify the bounded region, lightly shade it, and draw the axis of revolution. Draw in a rectangle which will help you determine dx or dy, disk/washer or shell, and the limits of integration.

With disk/washer, you need to identify big R and little r. With shell, you need p and h. A rectangle that is vertical requires integration with respect to x (dx) and a horizontal rectangle necessitates dy. You determine your limits based on how far along the axis the rectangles move. If it’s a dx problem, it’s the left and right x-values. If it’s a dy problem, it’s the y-value at the bottom and top.

I’m sure someone will come in and explain this better; I’m not great at teaching volume of solids of revolution.