Volume of a watermelon
Adjust the values of [math]a[/math] and [math]b[/math] until the purple function fits the top half of the watermelon well. Then uncheck "Show watermelon" and check "Show rotated region". |
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If you're not sure what to do next, you may find it helpful to experiment with the applet here: [url]http://higheredbcs.wiley.com/legacy/college/mccallum/0470131586/applets/ch8/hh_fig_8_16a.htm[/url] What's the volume of the watermelon? |
Volumes of Revolution with Disks/Washers (OLD)
[url=https://www.geogebra.org/m/acdsdq8g]Here's an updated version of this construction, taking advantage of GeoGebra's 3D capabilities[/url]. Just keeping this old attempt, constructed entirely in 2D, for posterity.[br]-------------------------------------------[br]This worksheet is intended to demonstrate the concepts behind the disk/washer method for calculating Volumes of Revolution.[br]Note that all the purple dots in the Graphics1 window are sliders. They don't snap to "clean" values as well as one may like, but precise computation is not the primary goal of the simulation.[br]The axis of revolution can be dragged either above or below the curves as long as f(x) forms the outer surface and g(x) forms the inner surface.[br]You may enter functions into the input fields or just drag the existing graphs in the Graphics1 window.[br]If you'd like to hide the highlighted disk/washer, just drag the highlight slider all the way to the left.[br]Acknowledged, the appearance is a bit cluttered, but hopefully the controls are found to be pretty intuitive.[br][br]Use of this simulation for scenarios in which human life is at stake is strictly prohibited.