Paul's Online Notes
Paul's Online Notes
Home / Calculus III / 3-Dimensional Space / Cylindrical Coordinates
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 12.12 : Cylindrical Coordinates

4. Convert the following equation written in Cylindrical coordinates into an equation in Cartesian coordinates.

\[z\,r = 2 - {r^2}\] Show Solution

There is not really a lot to do here other than plug in \(r = \sqrt {{x^2} + {y^2}} \) into the equation. Doing this is,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{z\,\sqrt {{x^2} + {y^2}} = 2 - \left( {{x^2} + {y^2}} \right)}}\]