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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