Formula for a Non-uniform Cylinder

[Eduardo Pinto]

Mentor note: moved from non homework thread to here hence no template.

Hi, I wanted to calculate a non standard Cylinder. It have a Height (h), with a base radius of (r1) and a top radius (r2). It varies linearly along the height. How can I come up with a formula for that? Since my girlfriend was Intrigued, I also wanted but I'm not sure how to come up with a formula for that.

 

[jedishrfu]

One method would be to use calculus to do it. Specifically Using volumes of revolution



And more volume of evolution videos may be found here

http://www.mathispower4u.com/calc-ii.php

 

[jedishrfu]

Wikipedia also has a discussion on how to do this

https://en.m.wikipedia.org/wiki/Solid_of_revolution

 

[Mark44]

Hi, I wanted to calculate a non standard Cylinder. It have a Height (h), with a base radius of (r1) and a top radius (r2). It varies linearly along the height.

Sounds like you're asking about what is called a frustum of a cone. There are formulas for the volume of such a figure. See https://en.wikipedia.org/wiki/Frustum

 

[mfb]

Calculate what? The volume? The surface? The center of mass? The moment of inertia? Something else?

In many cases you can treat it as cone minus a smaller cone.

 

[jedishrfu]

As an aside, here's a video on computing the surface area of a sphere:



If you ponder your problem in a similar way you might come up with a visual and intuitive way to solve your problem.

If not you can always use @mfb cone strategy and find the related formulas here:

https://en.wikipedia.org/wiki/Cone