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A right circular cone of height h’ is cut by a plane parallel to the base and at a distance h/3 from the vertex, then the volumes of the resulting cone and frustum are in the ratio:

  1. 1 : 3
  2. 8 : 19
  3. 1 : 4
  4. 1 : 7

 

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The sum of volumes of respective parts and the original cone will be same . Hence we have :

         1/3 π r2 h   =    1/3 π (2r/3)2 (2h/3)   +    x

  ==>  x              =     1/3  π  r2 h ( 1 - 8 / 27)

  ==>  x              =     1/3  π  r2 h  *  (19 / 27) 

Hence volume of frustum   =   1/3  π  r2 h  *  (19 / 27) 

Volume of smaller cone      =   1/3  π  r2 h  *  (8 / 27)

Hence ratio of volume smaller cone to frustum of cone  =   8 : 19

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