Oblique cylinder
Definition:
An oblique cylinder is one that 'leans over'  where the sides are not perpendicular to the bases. Opposite of a 'right cylinder'.
Try this
Drag the orange dot to reshape the cylinder. Note when it is a right cylinder and when it is oblique.
In an oblique cylinder, the bases (ends) remain parallel to each other, but the sides lean over at an angle that is not 90°.
If they are at right angles to the bases, it is called a right cylinder, and this is the kind we see most often, such as a soup can.
In the applet above, drag the orange dot to the left to create a right cylinder.
Volume
An interesting thing is that oblique cylinders have the same volume as a right cylinder of the same radius and height. The
height must be the perpendicular height, but as long as the radius and height are the same the volume does not change. To see this,
use the applet at Cylinder Volume. (Click on 'allow oblique' when you get there).
To see why this is, imagine the cylinder is composed of a set of thin discs, like coins. If you were to slide them sideways you would get an oblique cylinder shape, as in the figure on the right.
The volume of the discs does not change as you make it oblique, therefore the total volume remains constant.
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Related topics
(C) 2011 Copyright Math Open Reference. All rights reserved
