Question:If the surface area of two sphere are in the ratio of`4 : 25`then the ratio of their volumes is : 

A `4 : 25` 
B `25 : 4` 
C `125 :8` 
D `8 : 125` 

+ Answer
D 

+ Explanation
Let their radii be R and r. Then, 

`(πR^2)/(4πr^2)`

`= 4/25 ⇒ (R/r)^2`

`= (2/5)^2 or R/r`

`2/5.`

:. Ratio of their volumes

`= (4/3 πR^3)/(4/3 πr^3)`

`= (R/r)^3`

`= (2/5)^3`

`= 8/125`

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