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Q.

What is the volume of a sphere which is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere?


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a

4 5 π r 3  

b

4 3 r 3  

c

4 3 π r 3  

d

4 3 π r 2    

answer is C.

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Detailed Solution

Given- volume of a sphere which is equal to two-third of the volume of a cylinder.
Height and diameter of cylinder are equal to the diameter of the sphere.
Let d be the diameter of sphere and r be the radius of sphere.
Therefore, radius of cylinder=r
Height of cylinder=d=2r
This can be represented as,
Volume of sphere = 2 3  volume of cylinder   
                             = 2 3 2π r 3 = 4 3 π r 3  
Thus, the volume of sphere is 4 3 π r 3  .
Hence, option 3 is the correct option.
 
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