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Home » Show that the semi-vertical angle of the cone of the maximum value and of given slant height is tan ^−1√2
Show that the semi-vertical angle of the cone of the maximum value and of given slant height is tan ^−1√2
Applications of Derivatives | CBSE | Class 12 | Exercise 6.5 | Maths | NCERT
Show that the semi-vertical angle of the cone of the maximum value and of given slant height is tan ^−1√2

Let  be the radius,  be the height,  be the slant height of given cone and  be the semi-vertical angle of cone.

  

        ……….(i)

  Volume of the cone (V) =        ……….(ii)

  V = 

= 

  and 

Now 

 

 

 

 

At  

=    [Negative]

  V is maximum at 

  From eq. (i), 

 

  Semi-vertical angle, 

= 

  

i

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