Quantitative Aptitude Ques 2373
Question: Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circles. If the remaining area of the square is $ 168cm^{2}, $ then what is the size of the radius of the circle?
[IBPS RRB (Assistant Officers) 2015]
Options:
A) 14 cm
B) 1.4 cm
C) 35 cm
D) 21 cm
E) 3.5 cm
Show Answer
Answer:
Correct Answer: A
Solution:
- Let the radius of the circle be r cm.
$ \therefore $ Side of square will be 2r cm. Area covered by circles in the square $ =4\times \frac{1}{4}\pi r^{2}=\pi r^{2}cm^{2} $ Area of square $ ={{(2r)}^{2}}=4r^{2}cm^{2} $
$ \therefore $ Remaining area of square $ =4r^{2}-\pi r^{2} $
$ \Rightarrow $ $ 168=r^{2}( 4-\frac{22}{7} ) $
$ \Rightarrow $ $ 168=r^{2}( \frac{28-22}{7} )=\frac{6r^{2}}{7} $
$ \Rightarrow $ $ r^{2}=\frac{168\times 7}{6} $
$ \Rightarrow $ $ r^{2}=196 $
$ \Rightarrow $ $ r=14,cm $
BETA
