bonanova Posted December 17, 2013 Report Share Posted December 17, 2013 The front, side and top views of two objects give identical appearances. Object A appears in each case to be a square of side a. Object B appears in each case to be a circle of diameter a. If they are made of the same material, can you say which object is heavier? Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted December 17, 2013 Report Share Posted December 17, 2013 About its mass, yes. not so sure about its weight. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted December 18, 2013 Author Report Share Posted December 18, 2013 About its mass, yes. not so sure about its weight. the density of the material is 1. Then weight=mass. Now can you say which object is heavier? Quote Link to comment Share on other sites More sharing options...
0 harey Posted December 18, 2013 Report Share Posted December 18, 2013 (edited) 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 December 18, 2013 by harey Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted December 19, 2013 Author Report Share Posted December 19, 2013 By same material I implied same density. Suppose d=1 so volume = weight. Going a bit further just for fun, which object can weigh the most, and which can weight the least? Quote Link to comment Share on other sites More sharing options...
0 harey Posted December 20, 2013 Report Share Posted December 20, 2013 The circle is inscribed to the square... Going a bit further just for fun, which object can weigh the most, and which can weight the least? That's easy. The circle is inscribed to the square. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted December 20, 2013 Author Report Share Posted December 20, 2013 What if they were made of a thin film of small thickness d? Quote Link to comment Share on other sites More sharing options...
0 harey Posted December 20, 2013 Report Share Posted December 20, 2013 The best way is to make them of equal volume ( suppose what I call a "3D square" is a prism?): v_prism=a*a*d_prism v_cylinder=pi*a/2*a/2*d_cylinder => 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. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted December 20, 2013 Author Report Share Posted December 20, 2013 I thought of the lightest "cube" as three squares joined at a corner, Volume = 3a2d. The lightest "sphere" could be a "soap bubble'" Volume = pi a2d. In that sense, the "cube" could be the lighter of the two. Just a thought. Quote Link to comment Share on other sites More sharing options...
0 harey Posted December 21, 2013 Report Share Posted December 21, 2013 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". Quote Link to comment Share on other sites More sharing options...
Question
bonanova
The front, side and top views of two objects give identical appearances.
Object A appears in each case to be a square of side a.
Object B appears in each case to be a circle of diameter a.
If they are made of the same material, can you say which object is heavier?
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