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Q.

Two solid cones A and B are placed in a cylindrical tube as shown in figure below. The ratio of their capacities is 2:1. What is the height of cones?


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a

14 cm and 7 cm

b

15 cm and 8 cm

c

19 cm and 6 cm

d

20 cm and 4 cm 

answer is A.

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Detailed Solution

It is given that the ratio of the capacities of two solid cones A and B placed in a cylindrical tube are 2:1.
Finding the radius of the cone:
The diameter of the cone is 6cm.
r=d2=62=3cm
The volume of both the cones.
Let h 1   be the height of the first cone. Then the height of the second cone will be 21− h 1   . As the ratio of volume is 2:1, volume of the first cone is 2V and the volume of the second cone is V. So, for the first cone,
The volume of the cone of radius r and height h is , 1 3 π r 2 h   .
2V= 1 3 π r 2 h 2V= 1 3 π 3 2 h 1 V= 9 6 π h 1 V= 3 2 π h 1 …… 1  
 For second cone,
  V= 1 3 π r 2 h V= 1 3 π 3 2 21− h 1 V=3π 21− h 1              …… 2  
Comparing the equations (1) and (2) to determine the value of  h 1   .
3 2 π h 1 =3π 21− h 1   h 1 =2 21− h 1   3 h 1 =42 h 1 =14cm   Therefore, the height of the second cone is,
21− h 1 =21−14 h 1 =7cm  
Hence 1 is the correct option.
 
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