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Problem with 3 cones - wanted a symbolic solution

ValeryOchkov
24-Ruby IV
24-Ruby IV
‎May 28, 2019 08:19 AM
‎May 28, 2019 08:19 AM

Problem with 3 cones - wanted a symbolic solution

Here we have tried to find a symbolic solution for the problem of two cones.

But we can cut out three cones from a round billet!
We can show with the help of graphics and numerical mathematics that the third cone is superfluous - the maximum total volume can be only for two cones.
Can we show this using symbolic MATHEMATICS?
See please pics and Mathcad Prime 5.0 sheet.

Fig.1Fig.1Fig.2Fig.2Fig.3Fig.3Fig.4Fig.4Fig.5Fig.5Fig.6Fig.6Fig.7Fig.7Fig.8Fig.8Fig.9Fig.9Fig.10Fig.10

 

 
 
 

 

Cone.mcdx
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ValeryOchkov
24-Ruby IV
24-Ruby IV
(To:ValeryOchkov)
‎May 29, 2019 04:02 AM
‎May 29, 2019 04:02 AM

Here must be the triangle diagram

Fig. 11Fig. 11Fig. 12Fig. 12

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