RRB Technician 2014 Ques 12
Question: The ratio of the areas of the incircle and circumcircle of a square is
Options:
A) $ 1:2 $
B) $ 1:3 $
C) $ 2:1 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- Radius of circumcircle $ =\frac{1}{2} $ Diagonal of square $ =\frac{1}{2}\sqrt{2}a=\frac{a}{\sqrt{2}} $
$ \therefore $ Area of circumcircle $ =\frac{\pi a^{2}}{2} $ Radius of in circle $ =\frac{1}{2} $ of side of square $ =\frac{1}{2}a $
$ \therefore $ Area of in circle $ =\frac{\pi a^{2}}{4} $ Required ratio $ =\frac{\frac{\pi a^{2}}{4}}{\frac{\pi a^{2}}{2}}=\frac{1}{2}=1:2 $
BETA
