The object I had in mind is approximated by this bit of an old toothpaste tube. You can see that viewed at different angles it looks (roughly speaking) like a rectangle, a triangle, and a circle respectively. They are a bit sketch but hopefully you get the idea.
This is only proof-of-concept of course, but you should be able to convince yourself that with modelling clay or a 3D printer we could make a solid object that was indeed a rectangle from one angle, an equilateral triangle from the second and a circle from the third. And we could describe it mathematically and find its volume and surface area.
The Puzzling Object Revealed
See question here
The object I had in mind is approximated by this bit of an old toothpaste tube. You can see that viewed at different angles it looks (roughly speaking) like a rectangle, a triangle, and a circle respectively. They are a bit sketch but hopefully you get the idea.
This is only proof-of-concept of course, but you should be able to convince yourself that with modelling clay or a 3D printer we could make a solid object that was indeed a rectangle from one angle, an equilateral triangle from the second and a circle from the third. And we could describe it mathematically and find its volume and surface area.