the ratio of the areas incircle and circumcircle a square is..., Area, General Mathematics

Question:The ratio of the areas of the incircle and circumcircle of a square is :

A `1 : sqrt(2)` 
B `1 : sqrt(3)` 
C `1 : 4` 
D `1 : 2`

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+ AnswerD

+ ExplanationLet the side of the square be x. Then, its diagonal 

`= sqrt(2) x.`

:. Radius of incircle` = x/2` & radius of circumcircle 

`= sqrt(2x)/2 = x/sqrt(2)`

:. Required ratio

`= ((π x^2)/4 : (π x^2)/2)`

`= 1/4 : 1/2`

`= 1 : 2`.

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