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Two objects, Three views, Identical shapes



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What you make us to believe is a cube might be three "squares" of unknown thickness. (Appologies to the purists.)

What you make us to believe is a sphere might be three cylinders of unknown height.

Therefore, the volume cannot be calculated.

Besides, I leave the question open whether "made of the same material" implies the same density.

Edited by harey
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The best way is to make them of equal volume ( suppose what I call a "3D square" is a prism?):



=> d_cylinder=(4/pi)*d_prism

While it might work for small d, with growing d, it will became more and more perceptible that the cylinder should be a kind of barrel (or a pancake). The formulae get too complicated for my taste and my possibilities.

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Yes, I see. There must be a lot of solutions, like taking a sphere and a cube and drilling holes into the cube until it becames lighter than the sphere - no formula, no misscalculation.

My preferred solution is still that of the three squares and three pankaces in the planes xy, xz and yz.

BTW, the Volume=3a2d-d3 - I have the same oversight in my post n. 8.

I just wonder how often we make false deductions in the real life in the style "three projections=circle => it must be a sphere".

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