Find The Ratio Of Their Heights

If the volumes of two cones are in the ratio 1 : 4 and their diameter are in the ratio 4 : 5, then the ratio of their height is ( take p 22/7)

  1. 25 : 64
  2. 5 : 4
  3. 1 : 5
  4. 5 : 16
Anurag Mishra Professor Asked on 19th July 2015 in Maths.
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    Answer: (1) 25 : 64
    Explanation:-
    The ratio of volume of two cones = 1 : 4
    The ratio of diameter of cones = 4 : 5
    The ratio of radius of two cones = 2 :  5/2
    Formula-
    The volume of the cone = pai x r2 h/3
    Then, pai x (2)2 h/3 : pai x (5/2)2 h1 /3 = 1 : 4
    h/h1 = 1 x25/4 x 4 x 4
    h/h1 = 25/64
    h : h1 = 25 : 64
    Hence, the ratio of heights is 25 : 64.

    Anurag Mishra Professor Answered on 19th July 2015.
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