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Show that the right circular cone of least curve surface and given volume has an altitude equal to time the radius of the base.
Show that the right circular cone of least curve surface and given volume has an altitude equal to time the radius of the base.
Applications of Derivatives | CBSE | Class 12 | Exercise 6.5 | Maths | NCERT
Show that the right circular cone of least curve surface and given volume has an altitude equal to time the radius of the base.

 Let  be the radius and  be the height of the cone.

  Volume of the cone (V) = 

   (say) ……….(i)

And Surface area of the cone (S) = 

  (say) ….(ii)

 

= 

= 

   and 

Now 

 

 

 

    ……….(iii)

At   [Positive]

   is minimum when 

  From eq. (i), 

=  [From eq. (iii)]

 

 

Therefore, Surface area is minimum when height =  (radius of base)

i

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