Volumes (another perspective)

Posted: February 20, 2016 in Calculus: An Introduction, Integral Calculus, Volume
Tags: , , ,

This entry will no doubt get further under the skin of those who contend that I’m pushing things too far (and that is exactly why I’m publishing it).  This is a natural extension of the 2-dimensional analog in which circle area was derived. Cylindrical coordinates are identical to polar coordinates with a 3rd dimension thrown in. Directly below, the vertical dimension is governed by a linear function which results in a cone.

In the spirit of consistency, I’ve included a second example with which to draw comparisons to the first. Everything is identical between the two cases with one exception; the function which governs the vertical dimension in example two is that of a semi-circle.

 

Volume of a Cone

VolumeCone Cylindrical

Interact with cylindrical coordinates to see how the 3-dimensional sector changes.

 

Volume of a Sphere

VolumeSphere Cylindrical

 

Thanks for reading.

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