What is the height of a circular cone with surface line ("Mantellinie") s, which has the maximal volumina? My problem here is, that I am not really sure what surface line is..is this the same thing as just to say surface?

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What is the height of a circular cone with surface line (&quot;Mantellinie&quot;) s, which has the maximal volumina? My problem here is, that I am not really sure what surface line is..is this the same thing as just to say surface?

Jaida Sanders · Accepted Answer

The &quot;Mantellinie&quot;   s is what you think it is: It&#039;s the distance from the tip of the cone to the rim at the bottom. Given   s, you are free to choose the height h in the interval   [  0  ,  s  ], and the radius of the bottom circle will then be   r  =            s      2        −          h      2      . Therefore we have to maximize the function  V  (  h  )  =            π      3            r    2    h  =            π      3        (      s    2    h  −      h    3    )    (  0  ≤  h  ≤  s  )     .As   V  (  0  )  =  V  (  s  )  =  0 this maximum is taken for some   h  ∈     ]  0  ,  s  [    , which will come to the fore by solving       V    ′    (  h  )  =            π      3        (      s    2    −  3      h    2    )  =  0 for   h. There is only one solution in the interval       ]  0  ,  s  [    , namely  h  =            s              3                 ,and this is the height you wanted to know.

What is the height of a circular cone with surface

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