Formal methods are labourious. This tries to leverage dsm to do the heavy lifting.
A deliberately awkward sized truncated cone (TC).
Heavily compressed for posting the animation isn't great, so here are some steps:
- Enter Pull mode Extrude edge on the top edge of the cone and DSM will display a highlighted point showing the location of the cone's apex.
- Draw a point -- in 3D mode -- at that location.
- Enter Sketch mode on the centre line of the TC.
- Draw a line from the apex to the lower edge of the cone.
- Draw construction circles centred at the apex, to the lower and upper faces of the TC.
- Back in 3D, select the measure tool and copy the circumference measure to your caclulator, then press 'divide'.
- Back in DSM, measure and copy the circumference of the lower edge of the TC.
- Swicth back and paste to your calculator; then hit 'equals'.
- Multiply the result by 360°. Copy to clipboard. (This gives the arc angle of the flattened cone.)
- Back to DSM, re-enter sketch mode on the last plane.
- Draw a construction line from the apex, set the angle reference to the existing construction line, and complete to the outer most circle.
- Use the trim tool to remove the extraneous arcs and radial lines.
- Convert the remaining two arcs and two lines to non-construction lines.
- Return to 3D mode and the surface produced is your developed TC.
- Do something with it.