Summary

This activity is for a Calculus class to help students visualize how to calculate volume by the shells method. Students will be given a typical volume problem and create 5 to 7 cylinder shells to approximate the shape. Then they make the actual shape and calculate the volume.

This is the companion activity to Finding Volume: Disc Method http://www.thingiverse.com/thing:1711469

Print Settings

Printer Brand:

MakerBot

                                            <p class="detail-setting printer"><strong>Printer: </strong>                     <div><p>MakerBot Replicator</p></div></p>                                                                                <p class="detail-setting rafts"><strong>Rafts: </strong>                     <div><p>Yes</p></div></p>                                                                                <p class="detail-setting supports"><strong>Supports: </strong>                     <div><p>No</p></div></p>                                                                                <p class="detail-setting resolution"><strong>Resolution: </strong>                     <div><p>standard</p></div></p>                                                                                <p class="detail-setting infill"><strong>Infill: </strong>                     <div><p>10%</p></div></p>

How I Designed This

To create the rotated object and the cylinder shells I first got the 2 dimensional graph using desmos.com. Then I did a printscreen to capture the graph [figure 1]. I used an online SVG converter and opened it in 123d Design. I used the polyline tool to enclose the region [figure 2]. Then I used polyline again to draw a line acting as the y axis that this shape would get rotated over [Figure 3]. Next I drew rectangles at each interval point with a small width [Figure 4]. Then I used the revolve tool to rotate each rectangle around the line I drew [Figures 5 and 6]. To get the full object I revolved the whole graph around the line [Figure 7]. I also printed the object with a slice taken out so students can see the cross section. This was done by inserting a wedge and then subtracting it from the object [Figure 8].

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Finding Volume: Shell Method