Visualizing Solid Figures 5

To end this series of posts on visualizing solid figures, we will look at a problem that relates to how volumes of solid figures are formed. It has 5 parts which will be presented first. Then the solution will be given. Consider the region in the first quadrant bounded by the graphs of the parabola…

Visualizing Solid Figures 4

Volume by the method of “Cylindrical Shells” Today I will show you how to visualize the cylindrical shells used in computing the volume using Winplot. Winplot is a free program. Click here for Winplot and here for Winplot for Macs. For the example I will use the same situation as in the last post. This…

Challenge Answer

I posted a challenge question on March 28, 2013. Only one person, “April,”  replied with an explanation and it was a very good and succinct answer. You may read it here. The conundrum resulted from trying to calculate when a parabolic bowl was half full. Using the “disk” method there was one answer; using the “shell”…

Challenge

A student was asked to find the volume of the bowl-shaped figure generated when the curve y = x2 from x = 0 to x = 2 is revolved around the y-axis. She used the disk method and found the volume to be . To check her work she used the method of cylindrical shells…