question_answer

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 \[168\text{ }c{{m}^{2}},\]then what is the size of the radius of the circle?

[IBPS RRB (Assistant Officers) 2015]

A) 14 cm

B) 1.4 cm

C) 35 cm              

D) 21 cm

E) 3.5 cm

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

\[=4\times \frac{1}{4}\pi {{r}^{2}}=\pi {{r}^{2}}c{{m}^{2}}\]

Area of square \[={{(2r)}^{2}}=4{{r}^{2}}c{{m}^{2}}\]

\[\therefore \] Remaining area of square \[=4{{r}^{2}}-\pi {{r}^{2}}\]

\[\Rightarrow \]   \[168={{r}^{2}}\left( 4-\frac{22}{7} \right)\]

\[\Rightarrow \]   \[168={{r}^{2}}\left( \frac{28-22}{7} \right)=\frac{6{{r}^{2}}}{7}\]

\[\Rightarrow \]   \[{{r}^{2}}=\frac{168\times 7}{6}\]\[\Rightarrow \]\[{{r}^{2}}=196\]

\[\Rightarrow \]   \[r=14\,cm\]