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
Interact with cylindrical coordinates to see how the 3-dimensional sector changes.
Volume of a Sphere
Thanks for reading.
samuelson mathxp 