# Truncated Cone **URL:** \ **Category:** Factual Questions\ **Created:** [April 10, 2011, 7:35am UTC](https://boards.straightdope.com/t/truncated-cone/577850 "2011-04-10T07:35:23Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![Meme\_Chose](https://avatars.discourse-cdn.com/v4/letter/m/2acd7d/32.png) [@Meme\_Chose](https://boards.straightdope.com/u/Meme_Chose)\ **Post date:** [April 10, 2011, 7:35am UTC](https://boards.straightdope.com/t/truncated-cone/577850/1 "2011-04-10T07:35:23Z")
Is there a way to lay out a truncated cone of known dimensions using simple shapes–basically, circles, rectangles, and lines? I want to make a lampshade-shaped dealio in a basic vector drawing program, but using a height and diameters of my choosing. Let’s just say it will be 6 inches tall, 4" at the large end, and 2" at the small end. Note: I will want to do this multiple times with different dimensions, so I need a method rather than a solution. Note again: Math \> me. Please speak s l o w l y and use the idiot glossary. Thanks in advance. ---
**Author:** ![Reply](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/reply/32/15952_2.png) [@Reply](https://boards.straightdope.com/u/Reply)\ **Post date:** [April 10, 2011, 8:03am UTC](https://boards.straightdope.com/t/truncated-cone/577850/2 "2011-04-10T08:03:27Z")
You mean from a certain angle, like a perspective drawing? It might be easier to model it in 3D using something free and simple like [Google Sketchup](http://sketchup.google.com/) (truncated cone methods [one](http://vmancer.com/truncated-cone-google-sketchup-scale-tool/) or [two](http://vmancer.com/sketchup-truncated-cone-follow-me/)). Otherwise, if mathematical precision isn’t important, couldn’t you just draw two ovals and two lines? ---
**Author:** ![Meme\_Chose](https://avatars.discourse-cdn.com/v4/letter/m/2acd7d/32.png) [@Meme\_Chose](https://boards.straightdope.com/u/Meme_Chose)\ **Post date:** [April 10, 2011, 8:50am UTC](https://boards.straightdope.com/t/truncated-cone/577850/3 "2011-04-10T08:50:03Z")
It’s actually going to be a cutting file for a 3D paper project. SketchUp would be a great answer if I could “unroll” the model to a 2D drawing. Y’know, I just realized i can…in a way. Take one segment of the cone and copy/rotate it the required number of times. It should be way easier than working out the angles, anyway. Thanks for the inspiration! ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [April 10, 2011, 11:05am UTC](https://boards.straightdope.com/t/truncated-cone/577850/4 "2011-04-10T11:05:34Z")
Draw concentric 360 \* (D - d) / SQRT[(D-d)^2 + 4 h^2] degree arcs with radii of D \* SQRT[(D-d)^2 + 4 h^2] / (2 \* (D - d)) and d \* SQRT[(D-d)^2 + 4 h^2] / (2 \* (D - d)). Where D is the larger diameter, d is the smaller diameter, and h is the height. E.g. For the example you gave 2" diameter top, 4" diameter bottom, and 6" height. Use D = 4, d = 2, and h = 6 to find that you need to draw concentric 59.18 degree arcs with radii of 6.08" and 12.17". I drew a [picture](http://www.unc.edu/~schneidk/lampshade.jpg) which should help you make sense of the above. ---
**Author:** ![Meme\_Chose](https://avatars.discourse-cdn.com/v4/letter/m/2acd7d/32.png) [@Meme\_Chose](https://boards.straightdope.com/u/Meme_Chose)\ **Post date:** [April 10, 2011, 4:23pm UTC](https://boards.straightdope.com/t/truncated-cone/577850/5 "2011-04-10T16:23:50Z")
Thanks; that should be just what I need. Bonus points for you that I (mostly) understood it! I can’t actually measure degrees of arc in this program, but i should be able to fake it close enough for the intended purpose. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 10, 2011, 7:46pm UTC](https://boards.straightdope.com/t/truncated-cone/577850/6 "2011-04-10T19:46:47Z")
> [@](#): > > Draw concentric 360 \* (D - d) / SQRT[(D-d)^2 + 4 h^2] degree arcs with radii of D \* SQRT[(D-d)^2 + 4 h^2] / (2 \* (D - d)) and d \* SQRT[(D-d)^2 + 4 h^2] / (2 \* (D - d)). Where D is the larger diameter, d is the smaller diameter, and h is the height. That won’t work for what the OP wants: Concentric circles will make the truncation the same height everywhere. I think what the OP wants is for the cone to be truncated by a non-horizontal plane. ---
**Author:** ![Meme\_Chose](https://avatars.discourse-cdn.com/v4/letter/m/2acd7d/32.png) [@Meme\_Chose](https://boards.straightdope.com/u/Meme_Chose)\ **Post date:** [April 11, 2011, 6:14am UTC](https://boards.straightdope.com/t/truncated-cone/577850/7 "2011-04-11T06:14:06Z")
I haven’t worked out the math completely yet. Using the dimensions stipulated, my attempt at a spreadsheet to figure it returned a result of 29 degrees rather than 59. That resulted in mathy confusion and headache. However, the shape shown in the drawing Lance Turbo included is about right. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [April 11, 2011, 12:59pm UTC](https://boards.straightdope.com/t/truncated-cone/577850/8 "2011-04-11T12:59:00Z")
I’m glad you didn’t get frustrumated.