Question:Two cubes have their volumes in the ratio `8 : 27.` The ratio of the volume of the sphere to that of the cube is : 

A `2 : 3` 
B `3 : 2` 
C `4 : 9` 
D `64 : 729` 

+ Answer
C 

+ Explanation
Let their edges be a. Then,

`a^3/b^3 = 8/27 ⇔ (a/b)^3`

`= (2/3)^3 ⇔ a/b = 2/3`

`⇔ a^2/b^2 ⇔ 6a^2/6b^2 = 4/9.`

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Irin Moni

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