Relation between volume, diameter and height of right circular cone

The volumes of two right circular cones are in the ratio of 1:3 and their diameters are in the ratio of 3:5. The ratio of their height is

  1. 3 : 5
  2. 25 : 27
  3. 9 : 20
  4. 2 : 5
Manish Listener Asked on 31st October 2014 in Maths.
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  • 1 Answer(s)

    Answer: 25 : 27

    Solution:
    Volume of right circular cone, V = (1/3) πr2h
    Let us assume,
    Volume, height and radius for first right circular cone are : V1, h1 and r1  and V2, h2 and r2  for second cone.
    According to question,
    3V1 = V2 and
    5r1 = 3r2

    From eqn. 1

    3V1 = V2
    3 (1/3) π r12 h1 = (1/3) π r22 h2

    after solving this equation on both side

    r12 h1 = (1/3) r22 h2

    then put value from eqn. 2

    ((3/5) r2 )2 h1 = (1/3) r22 h2
    (9/25) r22 h1 = (1/3) r22 h2
    h1 = 1/3 * 25/9 h2   —- r22 was canceled on both side
    h1 = (25/27) h2

    Final Answer: Ratio of height of cone1 and cone2 is = 25 :  27

     

     

    Pushpendra Pal Dean Answered on 31st October 2014.
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