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Q.

A cone and a sphere have equal radii and equal volume. What is the ratio of the diameter of the sphere to the height of cone?


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a

0.9

b

0.8

c

0.5

d

0.25 

answer is C.

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Detailed Solution

It is given that, the cone and a sphere have equal radii and equal volume.
The volume of a circular cone is expressed as, V= 1 3 π r 2 h   , where r   be the radius of a circular cone.
The volume of a sphere is expressed as, V= 4 3 π r 3   , where r   be the radius of a sphere.
Thus,
1 3 π r 2 h= 4 3 π r 3 ⇒h=4r ⇒ h 2r = 2 1  
Since, diameter is d=2r   .
So,
⇒ h d = 2 1 ⇒ d h = 1 2 ⇒ d h =0.5  
Thus, the required ratio is 0.5   .
Therefore, option (3) is correct.
 
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