CAT 1994 | Question: 59

Question

Choose the best alternative:

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:

• A. 1 : 3
• B. 8 : 19
• C. 1 : 4
• D. 1 : 7

 

Answer 1

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