# Truncated cones

Hi, I’m trying to solve this “simple” exercise and I’m afraid I’m missing something. Anyone can help to solve it?? Thanks in advance. Alba

where is the drawing from ? any further info ?
if you cut a cone rectangular to the main axis you will get a circle. if not you will get an ellipse in your case …

check out

so starting from (a) diameter = 30 (circle) with the given angle - the next section (5/6) will not be a circle anymore - or do i miss something ?

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looks like it is not a diameter 30, 5/6, 2/3, 1/2 but just dimensions…

draw an inital Isosceles triangle (green) with those 15 degrees
_line
_rotate +/- 7.5 degree

Now draw an initial cut at the right 15-degree angle (red)
got to document properties and increase the display precision (not the unit tolerance)
_length will tell you, the red line is 33.68722mm
_scale with center at the tip of the triangle, scale factor is (33.68722 / 30)
you can calculate this directly in the commandline
result is the first cyan line.
now scale with 5/6, 2/3, 1/2 (copy = yes)
_mirror the magenta ones
(now you have all cutters - cyan)

draw an initial cone - most simple with
_revolve

_split the cone in top-View with the “cutters” (cyan)

use
_orient (can t handle 180-degree flip)
and
_orient3Pt (for the middle part)
to copy and arrange everything.

conic_02_tp.3dm (316.7 KB)

EDIT:
there is a file above with what I think is the solution ;-D

EDIT2
@martinsiegrist
updated a second interpretation / solution to above file.
scaling the initial approche in z direction you can get circles at the sections, the initial surfaces is a conical ellipse then. (while the first solution was a real cone and the sections where ellipses)

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It’s a trigonometry problem but it feels as though there’s some info missing…

Dear @Tom_P , that is exactly what I was trying to guess… No further info… And my knowledge about conic geometry tells me the same… We should get an ellipse instead of a circle…
I’m preparing some exercises for my students and, finding inspo, I just tried to solve this one that I found on internet and I couldn’t so… I posted just in case I was missing something…
Now that I see your next comment:
ok, super thanks Tom, I’m gonna take a deep look at your solution. I will let you know if I have any doubt about it.

Dear @Ncik yess… I just printed the screen shoot to measure the angles But this is a trick that a student can’t use in an exam for example, so that’s why I posted, just in case I miss any “hidden” info or there is a mathematical law that I miss at all… Thanks for your answer!

The plan says conic but it also says Ø…

I would claim conic is correct,
Ø is wrong - it is just a distance - see my post above.

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What if this pipe corner has to fit a circular flange at both ends?

as the sections are ellipse - a scale in z should modify above ellipse to circles… let me see … i ll update my post above

so you field tested the example to see how hard it is, and now that its confirmed that you can torture your students well enough they are going to go through hell? gee…

@encephalon lol! It’s been a test for me too

@Tom_P “Ø is wrong - it is just a distance”: agreed!! That was a comprehension mistake :s Shouldn’t take it literally. Thanks!